40 IS10 Abstracts

IP1

Approximate Inference in Graphical Models: TheFenchel Duality Perspective

Quite a number of problems involving inference from data,whether visual data or otherwise, can be set as a prob-lem of finding the most likely setting of variables of ajoint distribution over locally interacting variables. Theseinclude stereopsis, figure-ground segmentation, model-to-image matching, super-resolution, and so forth. Inferenceover locally interacting variables can be naturally repre-sented by a graphical model, however exact inference overgeneral graphs is computationally unwieldy. In the contextof approximate inference, I will describe a general schemefor message passing update rules based on the frameworkof Fenchel duality. Using the framework we derive allpast inference algorithms like the Belief Propagation sum-product and max-product, the Tree-Re-Weighted (TRW)model as well as new convergent algorithms for maximum-a-posteriori (MAP) and marginal estimation using ”convexfree energies”. Joint work with Tamir Hazan.

Amnon ShashuaThe Hebrew University of Jerusalem, Israelshashua@cs.huji.ac.il

IP2

Operator Splitting Techniques in Image Processing

Recently, operator splitting methods have been success-fully applied to various image processing tasks like the de-noising and deblurring of images also in the presence ofnon-additive noise, inpainting, sparse recovery problemsand multi-task learning. Splitting methods allow us to de-compose the original problem into subproblems which areeasier to solve.The talk reviews and relates various of theseoptimization methods from the point of view of averagedoperators, Bregman proximal point methods and primal-dual Lagrangian approaches. Attention is also paid to mul-tistep methods. Then, various examples are presented howsplitting algorithms can be successfully applied to imagerecovery problems.

Gabriele SteidlInstitute of Mathematics und Computer ScienceUniversitaet Mannheim, Germanysteidl@math.uni-mannheim.de

IP3

Data Don’t Lie: Image Processing Via Learned Ef-ficient Representations

In a large number of disciplines, image acquisition has ad-vanced much faster than image analysis. This permits toreplace a number of pre-defined concepts by learned ones.In particular, we can learn efficient image representations.Among these, sparse representations have recently drawnmuch attention from the signal processing and learningcommunities. The basic underlying model consist of con-sidering that natural images, or signals in general, admit asparse decomposition in some redundant dictionary. Thismeans that we can find a linear combination of a few atomsfrom the dictionary that lead to an efficient representationof the original signal. Recent results have shown that learn-ing (overcomplete) non-parametric dictionaries for imagerepresentations, instead of using off-the-shelf ones, sig-nificantly improves numerous image and video processingtasks. In this talk, I will first briefly present results onlearning multiscale overcomplete dictionaries for color im-

age and video restoration. I will present the frameworkand provide numerous examples showing state-of-the-artresults. I will then briefly show how to extend this to im-age classification, deriving energies and optimization pro-cedures that lead to learning non-parametric dictionariesfor sparse representations optimized for classification. Iwill conclude by showing results on the extension of this tosensing and the learning of incoherent dictionaries. Modelsderived from universal coding are presented as well. Thework I present in this talk is the result of great collabo-rations with J. Mairal, F. Rodriguez, J. Martin-Duarte, I.Ramirez, F. Lecumberry, F. Bach, M. Elad, J. Ponce, andA. Zisserman.

Guillermo SapiroUniversity of MinnesotaDept Electrical & Computer Engineeringguille@umn.edu

IP4

From Shape Matching to Shape Mechanics: Geom-etry and Dynamics

During the last decades, the study of shape spaces hasbeen driven by the accelerated development of imagingtechniques in biomedical engineering and the emergence ofcomputational anatomy. Starting from the basic and hardproblems of shape comparison, shape matching and mod-eling shape populations, a fascinating landscape is appear-ing involving infinite dimensional manifolds, Lie groups,Riemannian geometry, Hamiltonian systems and Statistics.Its connection with many existing mathematical theories,sometimes outside the usual scope of the imaging commu-nity, and the growing need for effective tools in shape anal-ysis, provide an exciting playground for inter-disciplinaryresearch and collaborations. This talks will visit somehot spots in this landscape and some challenges driven byanatomical growth modeling.

Alain TrouveEcole Normale Superieure, Francetrouve@cmla.ens-cachan.fr

IP5

The Inverse Problem of Seismic Velocities

To reasonable approximation, the construction of struc-tural images of the earth’s interior, using seismic reflec-tion data as input, boils down to an inverse problem forthe wave equation. This inverse problem requires that thespatially varying wave velocity (a coefficient in the waveequation) be determined from samples of solutions near theboundary of the space-time domain of propagation. Thedata-fitting techniques that have proven effective in otherscience and engineering inverse problems encounter funda-mental mathematical obstacles in application to this one.In response, the seismic prospecting industry has devised acollection of methods to extract earth structure from data,that appear at first glance to have little to do with data-fitting. I will describe the seismic inverse problem and thequalities that make it resistant to data-fitting, as well as anunderlying mathematical structure that encompasses boththe data-fitting and industrial approaches. This structuresupports variational principles, more general than the data-fitting or least squares principle, which in some cases haveproven effective tools for velocity estimation.

William SymesRice University

IS10 Abstracts 41

symes@caam.rice.edu

IP6

Compressed Sensing in Astronomy

The spatial infrared astronomical satellite Herschel,launched on May 14 2009, is the first satellite which hasa compressed sensing (CS) coder included in its on boardsoftware. We will present our motivations for using Com-pressed Sensing in this project. Then we will describe thepractical implementation of our CS coder/decoder. Wewill show from simulations that CS enables to recover datawith a spatial resolution enhanced up to 30% with similarsensitivity compared to the averaging technique proposedby ESA, and we will present preliminary results relativeto the CS performances on real Herschel data. Finallywe will show how other problems in astronomy such in-terferometric image deconvolution or gammay ray imagereconstruction can be also handled differently using CS.

Jean-Luc StarckLaboratoire AIM, CEA/DSM-CNRS-Universite ParisDiderotCEA Saclay, DAPNIA/SEDI-SAP, Serviced’Astrophysiquejstarck@cea.fr

CP1

Optimal Geometric Transformations of CompactManifolds

A fundamental mathematical problem underlying the sub-ject of matching and minimal morphing of images is theproblem of minimal distortion bending and morphing ofcompact manifolds. We consider cost functionals that mea-sure distortion of geometry produced by a diffeomorphismbetween two compact n-manifolds. Our cost functionalsmeasure the distortion in volume or the first (metric) andthe second (curvature) fundamental forms. We prove theexistence of the least distortion energy maps.

Oksana BihunConcordia College, Moorhead, MNobihun@cord.edu

CP1

A Fourth Order Nonlinear Pde-Based Image Reg-istration Model and Its Fast Algorithm

We first propose a new variational registration model usingfull curvature regularization, leading to superior results, forboth smooth and nonsmooth deformations, to competitorsincluding approximate curvatures of Fischer and Moder-sitzki (2003), Henn and Witsch (2005). Due to its non-linearity and high order, multigrid methods with standardsmoothers lead to non-convergence. We then propose aprimal-dual fixed point method as a new smoother to en-able fast convergence of a nonlinear multigrid. Variousnumerical experiments will be reported.

Noppadol ChumchobCentre for Mathematical Imaging Techniques andDepartment of Mathematical Sciences, University ofLiverpooln.chumchob@liverpool.ac.uk

Ke ChenUniversity of Liverpool

k.chen@liverpool.ac.uk

Carlos Brito-LoezaCentre for Mathematical Imaging Techniques andDepartment of Mathematical Sciences, University ofLiverpoolcbrito@liverpool.ac.uk

CP1

Method of Micromirrors For Catadioptric SensorDesign

We present a novel method for catadioptric sensor designwhich consists of a micromirror array, asymmetric mirrorand an orthographic camera. The micromirror method al-lows construction of any desired projection which was notpossible with single-mirror systems. We use Frobenius In-tegrability Theorem to write a system of quasilinear PDEs,whose numerical solution is the camera projection and nu-merically integrate the normal vector field to compute themirror surface.

Emek Kose CanLoyola Marymount Universityeksecan@lmu.edu

CP1

Topological Gradient for Image Restoration byAnisotropic Diffusion

Topological asymptotic analysis provides tools to detectedges and their orientation. The purpose of this workis to show the possibilities of anisotropic topological gra-dient in image restoration. Previous methods based onthe topological gradient used isotropic diffusion to restorethe image. These methods are improved here by usinganisotropic diffusion, a texture detector and differentiat-ing between principal and secondary edges. Numerical re-sults are presented, including a comparison with Non-LocalMeans method.

Stanislas Larnier, Jerome FehrenbachUniversite Paul SabatierInstitut de Mathematiques de Toulousestanislas.larnier@math.univ-toulouse.fr,jerome.fehrenbach@math.univ-toulouse.fr

CP1

Robust Optical Flow for Modeling Dynamical Sys-tems

Classical optical flow techniques assume conservation of in-tensity and a smoothness of the flow field. If these assump-tions are dropped, such techniques can be used to computeapparent flows between time snapshots of data that doesnot come from images, even if these flows are turbulent anddivergent. We present a variational optical flow approachbased on the continuity equation and total-variation div-curl regularization for computing the flow fields betweenspecies densities generated from a two-species predator-prey model. Though the dynamics of the model systemcould be analyzed mathematically from the model itself,using an optical flow approach allows to apply dynamicsanalysis methods directly to measured data, even in theabsence of an a priori model.

Aaron B. LuttmanClarkson University

42 IS10 Abstracts

Department of Mathematicsaluttman@clarkson.edu

Erik Bollt, Ranil Basnayake, Sean KramerClarkson Universitybolltem@clarkson.edu, basnayakeranil80@gmail.com,kramersj@clarkson.edu

CP1

The Image Editing Pde’s

Poisson image editing techniques involve the solution of aPoisson equation where the second member is a modifiedgradient field. Application are numerous: adding, remov-ing objects, fusing images, deblocking, local contrast adjus-tament, etc. In this communication we review the manyrecently proposed variants, give their asymptotic isotropicversion, and show how all of them can recieve a fast imple-mentation. The asymptotic equations results will be shownon several significant experiments.

Ana B. PetroUniversitat de les Illes Balearsanabelen.petro@uib.es

Jean-Michel MorelENS Cachanmorel@cmla.ens-cachan.fr

Catalina SbertUniversitat de les Illes Balearscatalina.sbert@uib.es

CP1

The Minkowski Functionals: An Objective Tool toQuantify Typeface Legibility

Text legibility is function of numerous elements such as thespecific typeface (serif or sans serif), the character heightor the interletter spacing. The experiments assessing leg-ibility have been greatly impacted by the choice of hu-man participants in the reading tests. We propose usingMinkowski functionals, which are widely used to describecomplex morphologies, to quantify the image of a text af-ter erosion and dilatation. We bring out the role played byserifs.

Jean F. PoiraudeauIUT, Limoges Universitypoiraudeau@unilim.fr

Isabelle BlasquezLimoges Universityisabelle.blasquez@unilim.fr

Pierre fournierLICN-IUT du Limousinpierre.fournier@unilim.fr

CP2

Optimal Dynamic Tomography for Wide-SenseStationary Spatial Random Fields

We present a new method to reconstruct a time-varyingobject modeled as a wide-sense stationary spatial ran-dom field from its tomographic projections. The optimalreconstruction method combines aspects of the Kalman

and Wiener filters, but the computational complexity isthe same as filtered backprojection. Applications of thismethod include biomedical imaging under rigid-body pa-tient motion and problems with motion described by linearshift-invariant partial differential equations, including ad-vection and diffusion.

Mark Butala, Farzad KamalabadiUniversity of Illinois at Urbana-Champaignbutala@illinois.edu, farzadk@illinois.edu

CP2

Computing Tomographic Projection Operators onUnstructured Meshes

For tomography problems on unstructured meshes, e.g.,those from limited angle tomography, it is desirable to com-pute algebraic solutions. Algebraic reconstruction tech-niques require computation of discrete approximations ofprojection operators, traditionally a difficult task on un-structured meshes. We present a novel ray tracing algo-rithm for computing such operators on a recursive meshdata structure. We show that this method works in arbi-trary dimension and discuss its scalability relative to themesh diameter. We also present a straightforward parallelextension to our algorithm.

Russell J. HewettUniversity of Illinois at Urbana-Champaignrhewett2@illinois.edu

William CochranOak Ridge National Laboratorywkcochran@gmail.com

CP2

Time-Dependent Tomographic Imaging of the So-lar Atmosphere

Solar coronal tomography is concerned with reconstructingthe volumetric structure of the inner atmosphere of the Sunbased on a series of 2-D projection observations. We usea Monte Carlo approximation to the Kalman filter to es-timate time dependent 3-D reconstructions that are morephysically correct and significantly more efficient to com-pute than those from classical time-invariant techniques.Empirical reconstructions of the coronal electron densitydistribution from this algorithm will be presented.

Farzad Kamalabadi, Russell J. Hewett, Mark ButalaUniversity of Illinois at Urbana-Champaignfarzadk@illinois.edu, rhewett2@illinois.edu,butala@uiuc.edu

CP2

Resistor Networks and Optimal Grids for the Elec-trical Impedance Tomography with Partial Bound-ary Measurements.

Electrical impedance tomography with partial boundarymeasurements is a problem of finding the electrical con-ductivity inside a domain from simultaneous measurementsof voltages and currents on a part of its boundary. Evenin the case of full boundary measurements the problemis severely ill-conditioned. We solve the EIT with partialmeasurements using a numerical method based on the the-ory of resistor networks and optimal grids, which does notrequire explicit regularization. Two distinct variations of

IS10 Abstracts 43

the method based on different resistor network topologiesand the theory of extremal quasiconformal mappings arepresented.

Alexander V. Mamonov, Liliana BorceaRice Universitymamon@rice.edu, borcea@rice.edu

Vladimir DruskinSchlumberger Doll Researchdruskin1@slb.com

CP2

Detection and Imaging Objects Buried Under aRough Interface Through Experimental Data

The inverse scattering problem whose aim is to detect andimage the objects buried under a rough surface is solvedand verified with the experimental data. By using the datawhich are collected through measurements performed on aline in the region not containing the bodies, it is first de-tected and located the objects via the surface impedancemodelling. The surface impedance is calculated by ana-lytically continuing the data to the rough interface. Thenthe contrast source extended Born approach is applied forthe imaging of the objects, which requires to solve a cou-pled system of integral equations. The Green function ofthe background media containing rough interface,which ap-pear in the integral equations, is calculated through BuriedObject Approach.

Hulya SahinturkYildiz Technical Universityhsahin@yildiz.edu.tr

Ibrahim AkdumanIstanbul Technical UniversityElectrical and Electronics Eng. Facultyakduman@itu.edu.tr

CP2

Shape-Based Methods for Vector-Valued InverseProblems with Highly Inhomogeneous, UnknownBackgrounds

A variational formulation is developed for the recovery ofmultiple physical properties in an inverse problems con-text. A new, low-order parametric level set technique isemployed to represent targets of interest embedded in aninhomogeneous unknown background. Accurate recoveryof this background is achieved through the use of a novelregularization scheme coupling the multiple parameters ofinterest. The approach is validated for a dual energy X-rayCT problem arising in an airport security application.

Oguz SemerciTufts Universityoguz.semerci@gmail.com

CP3

Construction of Boundary Wavelets

We present a new approach for constructing boundaryfunctions for wavelets and multiwavelets on a finite inter-val. The construction is unique up to the choice of somearbitrary orthogonal matrices. In the preceding talk Reg-ularity Properties of Boundary Wavelets we derived con-ditions for continuity and approximation order. We show

how to use these conditions to reduce the arbitrariness, andto construct boundary functions with desired properties.

Ahmet AlturkIowa State Universityaalturk@iastate.edu

Fritz KeinertDept. of MathematicsIowa State Universitykeinert@iastate.edu

CP3

Discrete Symbol Calculus, a New Numerical Toolfor Wave-Based Imaging

Most linear operators that are somehow related to wavepropagation have an oscillatory integral representationthat can be compressed by means of low-rank expansionsof so-called symbols. We start by explaining this idea andits implication for the numerical precomputation of func-tions of operators. We then show that this strategy yields asensible way of numerically inverting the so-called normaloperator, or wave-equation Hessian, in reflection seismol-ogy. Work in collaboration with Lexing Ying (UT Austin)and Nicolas Boumal (MIT).

Laurent DemanetMathematics, MITdemanet@gmail.com

CP3

Regularity Properties of Boundary Wavelets

Boundary functions for wavelets and multiwavelets on a fi-nite interval are usually constructed as linear combinationsof standard (interior) scaling functions. Such boundaryfunctions obviously inherit the smoothness properties ofthe interior functions. Boundary functions can also be con-structed directly from recursion relations. We derive con-tinuity and approximation order conditions for this case.This approach leads to new kinds of boundary functions,and lays the groundwork for the following talk on construc-tion of boundary wavelets.

Fritz KeinertDept. of MathematicsIowa State Universitykeinert@iastate.edu

Ahmet AlturkIowa State Universityaalturk@iastate.edu

CP3

Optimal Design for Imaging

Experimental design is an important topic for imaging sci-ence. It has broad applications in the areas of physics, biol-ogy and engineering. In this talk, we examine the BayesianA and Aπ optimal designs. Our methods have the capa-bility to improve the image quality while maintaining lowexperimental cost. Several imaging experiments, such assuper resolution will be presented. Moreover, we exploreefficient methods for large scale design problems.

Zhuojun MagnantDepartment of Mathematics and Computer Science

44 IS10 Abstracts

Emory Universityztang4@emory.edu

Eldad HaberDepartment of MathematicsThe University of British Columbiahaber@math.ubc.ca

Luis TenorioColorado School of Minesltenorio@mines.edu

CP3

A Segmentation Boosted Denoising Scheme for Im-ages with Excessive and Inhomogeneous Noise

Image denoising is an important pre-processing step. It be-comes a challenging task when the image contains excessiveand inhomogeous noise. It is especially hard to balance thepreservation of features and removal of spatially variantnoise. To remove excessive noise, a single image denois-ing scheme usually leads to blurry images. We propose amethod to take full advantage of information from segmen-tation. The idea is explained using NL-Means framework.We use the original NL-Means to obtain an intermediateresult on which to apply segementation. The intensitiesand noise variances inside and outside the segmented ob-jects are then used to adaptive define search windows andsmoothing parameters. They are utilied to the noisy im-age to obtain a clean and sharp image. The search windowsdo not have a fixed geometry, they are however adaptivelychosen inside or outside the objects to ensure identicallyidenpendent distributed assumption to be better satisfied.Noise variances are calculated pointwisely to deal with in-homogenity of noise. The proposed denoising scheme isfast and results in sharper images while removing exces-sive noise.

Weihong GuoDepartment of Mathematics, Case Western ReserveUniversitywxg49@case.edu

Jing QinCase Western Reserve Universityjxq26@case.edu

CP3

Analytical and Computational Methods for Trans-mission Eigenvalues

The interior transmission problem is a boundary valueproblem that arises in the scattering of time-harmonicwaves by an inhomogeneous medium of compact support.The associated transmission eigenvalue problem has impor-tant applications in qualitative methods in inverse scatter-ing theory. In this talk, we first establish optimal condi-tions for the existence of transmission eigenvalues for aspherically stratified medium and give numerical exam-ples of the existence of both real and complex transmis-sion eigenvalues in this case. We then propose three finiteelement methods for the computation of the transmissioneigenvalues for the cases of a general non-stratified mediumand use these methods to determine the accuracy of re-cently established inequalities for transmission eigenvalues.

Jiguang SunDepartment of Mathematics, Delaware State University

sunjiguang@yahoo.com

Peter B. MonkDepartment of Mathematical SciencesUniversity of Delawaremonk@math.udel.edu

Colton DavidUniversity of Delawarecolton@math.udel.edu

CP3

Reconstruction from Non-Uniform Spectral Data

We discuss the reconstruction of compactly supportedpiecewise-smooth functions from non-uniform samples oftheir Fourier transform. This problem is of relevance inapplications such as magnetic resonance imaging (MRI).We address the issue of non-uniform sampling density andits effect on reconstruction quality. We compare classicalreconstruction approaches with alternate methods such asspectral re-projection and methods incorporating jump in-formation.

Adityavikram Viswanathan, Douglas CochranSchool of Electrical, Computer and Energy EngineeringArizona State Universityaditya.v@asu.edu, cochran@asu.edu

Anne GelbArizona State Universityag@math.la.asu.edu

Rosemary A. RenautArizona State UniversitySchool of Mathematical and Statistical Sciencesrenaut@asu.edu

CP4

Parametric Level Set Methods for Inverse Prob-lems

PDE-based level set methods have difficulties in determin-ing object structure for ill-posed inverse problems. A lackof sensitivity can slow convergence. Grid-based represen-tations lead to frequent re-initialization or the use of ad-ditional terms in the underlying cost function. We employa parametric representation of the level set function usingan adaptive expansion of compactly supported radial basisfunction that addresses these difficulties. Results are pre-sented using an electrical impedance tomography problemarising in environmental remediation.

Alireza Aghasi, Eric MillerTufts Universityalireza.aghasi@tufts.edu, elmiller@ece.tufts.edu

CP4

Recovering the Location, Size, and Grade of a Car-diac Ischemia Using Level Set Methods

We present a level set strategy for recovering the character-istics of a cardiac ischemic region. Cardiac electrical activ-ity is modeled in 2-D with diffusion-reaction equations withdifferent electrical behavior for the ischemic region and forthe surrounding healthy tissue. Measurements are takenby electrodes outside of the cardiac membrane. Numericalexperiments show that the proposed strategy may stand for

IS10 Abstracts 45

a practical algorithm to extract the diagnosis informationof cardiac ischemia.

Diego AlvarezUniversidad Carlos III de Madridjdiego@math.uc3m.es

Felipe Alonso-Atienza, Jose Luis Rojo-AlvarezUniversidad Rey Juan Carlosfelipe.alonso@urjc.es, joseluis.rojo@urjc.es

Miguel MoscosoUniversidad Carlos III de Madridmoscoso@math.uc3m.es

CP4

Imaging Localized Scatterers with Singular ValueDecomposition and �1 Optimization

We consider narrow band array imaging of localized scat-terers using the singular value decomposition (SVD) and �1minimization and compare the results with other imagingmethods such as multiple signal classification (MUSIC).We show that well-separated point scatterers can be re-covered exactly with �1 optimization. Moreover, using theSVD we determine optimally subsampled array data forthe �1 optimization. Numerical simulations indicate thatthis imaging approach is robust with respect to additivenoise. If time permits, I will discuss comparison of differ-ent imaging methods in random medium.

Anwei ChaiInstitute for Computational and MathematicalEngineeringStanford Universityanwei@stanford.edu

George C. PapanicolaouStanford UniversityDepartment of Mathematicspapanico@math.stanford.edu

CP4

Regularization Parameter Selection for Penalized-Maximum Likelihood Estimation Methods in Pet.

PET data consists of counts of photons originating fromrandom events, resulting in data-noise that is well-modeledby a Poisson distribution. Since the associated Poissonmaximum likelihood estimation problem is ill-posed, reg-ularization is needed. Regularized Poisson maximum like-lihood estimation has been extensively studied by the au-thors, however, the essential problem of choosing the regu-larization parameter remains unaddressed. In this talk, wepresent three statistically motivated methods for choosingthe regularization parameter. Numerical examples will bepresented to test these methods.

John GoldesDepartment of Mathematical SciencesUniversity of Montanajohn.goldes@umontana.edu

CP4

Numerical Inversion of the Spherical Mean ValueOperator

We are concerned with the numerical inversion of the spher-

ical mean value operator on the torus, which is the corner-stone of some recent imaging methods like photoacoustictomography. We give a singular value decomposition ofthe this operator and characterize its range in terms ofSobolev spaces. Furthermore, we present a fast, Fourierbased algorithm for its numerical evaluation, give boundsfor the discretization error, and compare our algorithm toquadrature based algorithms.

Ralf HielscherTechnische Universitat Chemnitz, Germanyralf.hielscher@gmail.com

CP4

A Level Set Approach for Fluorescence LifetimeTomography in Turbid Media

The problem of fluorescence lifetime imaging involves thereconstruction of the spatial distribution of the fluorescencedecay rates within the tissue simples from boundary data.In several centimiter thick tissue this problem poses severalchallenges. In the direct problem one must account formultiple scattering of light in tissue, and in the inverseproblem for the deconvolution of the pulse dispersion inthe tissue and the fluorescence decay rates. In this talkwe present an algorithm that is a hybridization of the levelset technique for recovering the distributions of distinctfluorescent markers with a gradient method for estimatingtheir lifetimes.

Miguel Moscoso, Diego Alvarez, Paul MedinaUniversidad Carlos III de Madridmoscoso@math.uc3m.es, jdiego@math.uc3m.es, pmed-ina@math.uc3m.es

CP5

Image Processing Techniques for Assessing Con-tractility in Isolated Adult and Neonatal CardiacMyocytes

We describe two computational frameworks to assess thecontractile responses of enzymatically dissociated adultand neonatal cardiac myocytes. Our results demonstratethe effectiveness of the approaches in characterizing thetrue ”shortening” in the contraction process. The meth-ods provide comprehensive assessment of the contractionprocess, and can potentially eliminate errors caused by ro-tation or translation. Changes due to drug intervention,disease modeling, transgeneity, or other common applica-tions to mammalian cardiocytes can be evaluated.

Peter BlomgrenSan Diego State UniversityDepartment of Mathematics and Statisticsblomgren@terminus.sdsu.edu

Carlos BazanSan Diego State UniversityComputational Science Research Centercarlos@carlosbazan.com

David TorresComputational Science Research CenterSan Diego State Universitycacho5us@hotmail.com

Paul PaoliniDepartment of BiologySan Diego State University

46 IS10 Abstracts

ppaolini@sunstroke.sdsu.edu

CP5

Atlas Based Mri Segmentation Using Both Magni-tude and Phase Information

We present a new framework for MR image segmentationbased on deformable template using both the magnitudeand phase information. In VASO MRI, the phase dependson tissue type, provides extra information about objectboundaries. Hence using phase information will improvethe segmentation and analysis of MR images. Finding theoptimal mapping is formulated as a variational problemover a vector field.

Yan CaoThe University of Texas at DallasDepartment of Mathematical Sciencesyan.cao@utdallas.edu

Jinsoo Uh, Hanzhang LuUT Southwestern Medical Centerjinsoo.uh@utsouthwestern.edu,hanzhang.lu@utsouthwestern.edu

CP5

Physics-Based Image Segmentation for EndoscopicImages

We propose a new mathematical model for analyzing endo-scopic images, which are obtained in vivo by chromoscopiccolonoscopy. The model is based on a PDE-constrainedoptimization problem, in which the state equation repre-sents the chromoscopy process and the objective functionuses the Chan and Vese segmentation model.

Isabel N. FigueiredoUniversity of Coimbraisabelf@mat.uc.pt

Omar Ghattas, Georg StadlerUniversity of Texas at Austinomar@ices.utexas.edu, georgst@ices.utexas.edu

Pedro FigueiredoFaculty of Medicine, University of CoimbraPortugalpedro.n.figueiredo@clix.pt

Nuno AlmeidaDepartment of GastroenterologyUniversity Hospital of Coimbra, Portugalnuno.p.almeida@clix.pt

CP5

Probabilistic Identification and Estimation of Noise(piesno): Mathematical Features and Challenges

PIESNO is a recent technique of noise assessment for mag-netic resonance imaging that has provided new approach toidentifying noise-only pixels and to estimating noise levelin magnitude images. This technique embodies commonfeatures from different fields such as probability and dy-namical system. Here, we will outline these interestingfeatures and discuss key mathematical challenges associ-ated with this framework that are currently not tractable

through analytical means.

Cheng Guan Koay, Evren OzarslanSection on Tissue Biophysics and Biomimetics, NICHDNational Institutes of Healthguankoac@mail.nih.gov, ozarslev@mail.nih.gov

Peter J. BasserNational Institutes of Healthpjbasser@helix.nih.gov

Carlo PierpaoliSection on Tissue Biophysics and Biomimetics, NICHDNational Institutes of Healthcarlo@helix.nih.gov

CP5

Detecting Jump Discontinuities Given NoisyFourier Data

The detection of jump discontinuities in physical space us-ing frequency (Fourier) data is an essential aspect of Medi-cal Resonance Image processing. The difficulty of the tasklies in extracting local information from the global Fourierdata, and is further complicated by noise. In this talk, wediscuss a recently developed algorithm that uses frequencydata to recover the jump discontinuities. The expected ac-curacy of the detector has been modeled using statisticalhypothesis testing.

Alexander M. PetersenArizona State Universityalxpetersen@gmail.com

CP5

A Study of Chiari Malformations Using MagneticResonance Elastography

Magnetic Resonance Elastography (MRE), also called pal-pation by imaging, is a non-invasive, in vivo imaging tech-nique used to measure the elasticity of a biological tissuesubject to dynamic or static mechanical stress. The result-ing strains are measured using magnetic resonance imaging(MRI) and the related elastic modulus is computed frommodels of tissue mechanics. Such a technique can be usednot only as a non-invasive diagnostic tool for tumor detec-tion, but also for gaining fundamental knowledge about thein vivo mechanical properties of normal biological tissues.In particular, brain MRE using the natural pulsations ofthe brain will help us better understand the brain mechan-ics. The present proposal will involve using magnetic res-onance images from Hershey College of Medicine of brainsof patients with chiari malformations. We plan to analyzehow the presence of this malformation changes the stiffnessof the brain tissue in the vicinity of the malformation. Thedesign aim of the proposal is to develop a computationaltool in Matlab capable to study the mechanical proper-ties of the brain tissue with chiari malformations beforeand after the surgery using medical images and appropri-ate mechanical models for the brain.

Osman VeledarThe Penn State Universityozv101@psu.edu

Corina DrapacaDepartment of Engineering Science and MechanicsPennsylvania State Universitycsd12@psu.edu

IS10 Abstracts 47

CP5

Fast Algorithm for Sensitivity Encoding with Ar-bitrary K-Space Trajectories

Speed is a crucial issue in MR imaging for clinical appli-cations. We propose a fast numerical algorithm for Sensi-tivity Encoding in partial parallel imaging with arbitraryk-space trajectories. The proposed method is an integra-tion of the variable-splitting and penalty techniques (VSP)with Barzilai-Borwein (BB) gradient method. VSP formu-lates the original model as an unconstrained minimizationproblem, which can be split into two subproblems: TVdenoising and linear inversion. The former can be solvedefficiently using recently developed methods, whereas theoptimal solution for the latter can be quickly approximatedby using BB method. Continuation scheme is also used toimprove the practical performance. Comparisons with var-ious recently proposed methods indicate the outstandingefficiency of our algorithm with state-of-the-art reconstruc-tion effects. Our method can be extended to any TV/L1image reconstruction problems.

Xiaojing YeDepartment of Mathematics, University of Florida358 Little Hall, Gainesville, FL32611-8105xye@ufl.edu

Dzung PhanDepartment of MathematicsUniversity of Floridadphan@ufl.edu

Yunmei ChenUniversity of Floridayun@math.ufl.edu

Feng HuangInvivo Corporation, Philips HealthCare, Gainesville, FLf.huang@philips.com

CP6

A New Model for Deblurring Images

We propose a new model for recovering an image from ablurry observation. This model is based on a new form ofthe blur operator and consists to solve a particular opti-mization problem which is intimately linked to the momentproblem. We combine recent mathematical results on mo-ments and semidefinite programming to provide a reliableskill for deblurring images. The methodology allows tohandle isotropic and anisotropic blur.

Tahar Zamene BoulmezaoudLaboratoire de Mathematiques de VersaillesUniversity of Versailles SQYboulmezaoud@math.uvsq.fr

Mohamed El RhabiRealeyes 3D Corp.Saint-Cloud, Franceelrhabi@gmail.com

Gilles RochefortRealEyes3Dgrochefort@realeyes3d.com

CP6

Counterexamples in Image Deconvolution

Image deconvolution requires regularization. This talk willsurvey a number of reasonable regularization approachesthat nevertheless lead to unsatisfactory results.

Alfred S. CarassoNat’l Inst of Standards & Techalfred.carasso@nist.gov

CP6

Parallel Denoising

New frontiers of science are creating huge demands on com-putational imaging. Biological studies aiming to reveal theinner works of cells and cell-to-cell interactions rely on ul-tra resolution images to observe when, where, and how acell develops so we can understand with the help of fac-tual observations the entire mechanisms of cell regulation.Astronomy will enourmesly benefit from the planned 3.2Gigapixel camera of the Large Synoptic Survey Telescope.The project will generate images of the sky covering bil-lions of galaxies and stars at a rate of 15 Terabytes pernight. In both situations fast and reliable image process-ing is required to render solutions in a reasonable time. Tocope with such challenging processing demands we devel-oped NOIR, Nonlinear Image Restoration software. NOIRis a parallel image denoising algorithm and software capa-ble of filtering images at an approximate rate of 3.5 millionpixels per second on a commodity 16 cores computer. Itis based on our rewriting of the nonlocal means filter. Wewill present our algorithm and show how we make such aremarkable filter useful for projects in Biology, Astronomy,and Materials Science.

Alexandre CunhaCalifornia Institute of Technologycunha@caltech.edu

Jerome DarbonUCLAjerome@math.ucla.edu

CP6

A Robust Method for Joint Correction of Nonuni-form Illumination and Blind Deconvolution of Bar-code Signals

This paper deals with a joint nonuniform illumination esti-mation and blind deconvolution for barcode signals. Suchoptimization problems are highly non convex. A robustmethod is needed in case of noisy and blurred signals anduneven illumination. Here, we present a novel methodbased on a genetic algorithm combining discrete and con-tinuous optimization. It is successfully applied to real dataswith strong noise. A comparison with a non local gradientbased method is also provided.

Laurent DumasUniversite Pierre et Marie Curie Paris 6dumas@ann.jussieu.fr

Mohammed El Rhabi, Gilles RochefortRealEyes3Dmelrhabi@realeyes3d.com, grochefort@realeyes3d.com

48 IS10 Abstracts

CP6

Image Denoising and Restoration by ConstrainedRegularization

In this work we present a new iterative algorithm for imagedeblurring and denoising. The algorithm is based on thesolution of the constrained least squares problem:

min ‖Hx − yδ‖2 s.t. R(§) ≤ γ, γ > ′

where the smoothness constraint γ is computed by an ef-ficient low pass filtered version of the noisy data yδ. Theiterations compute an approximate value of the Lagrangemultiplier λ and the solution x(λ). The method has beenwidely tested with different regularization functions R(§)in case of gray levels and color images.

Fabiana ZamaDepartment of Mathematics, University of Bolognazama@dm.unibo.it

Elena Loli PiccolominiDepartment of Mathematics,University of Bolognapiccolom@dm.unibo.it

CP6

Blind Restoration from Mild Blur and Heavy Noise

We present a non-iterative algorithm for blind restorationof an image which has been corrupted by mild blur, andstrong noise. The most successful deblurring algorithms todate address the problem in a setting where the corruptingnoise is assumed so small as to be essentially negligible. Un-fortunately, in practical applications, much stronger noiseis often present, which renders most algorithms useless.Furthermore, it is often the case that most images we wishto enhance in practice suffer from mild, rather than severeblur. This motivates our study, where we develop a lo-cally adaptive and non-parametric method for high fidelityenhancement of such distorted images. We illustrate thatour algorithm can produce state of the art results underpractical imaging conditions.

Xiang ZhuUniversity of California, Santa Cruzxzhu@soe.ucsc.edu

Peyman MilanfarEE DepartmentUniversity of California, Santa Cruzmilanfar@ee.ucsc.edu

CP7

Tracking and Autofocus in Synthetic ApertureRadar Imaging

From first principles, we develop a synthetic aperture radarimaging method that includes both motion estimation oftargets and radar platform trajectory estimation. Themethod uses both the Wigner transform and ambiguityfunction of the radar data and preliminary images, prop-erly segmented over sub-apertures, to derive estimates forthe target motion and platform perturbations. This ap-proach produces an iterative method to construct autofo-cused high-resolution images over wide apertures, applica-ble to X-band persistent surveillance SAR.

Thomas Callaghan

Institute for Computational and MathematicalEngineeringStanford Universitytscallag@stanford.edu

CP7

Compressed Sensing Synthetic Aperture RadarImaging

We introduce a new Synthetic Aperture Radar (SAR)imaging modality which can provide a high resolution mapof the spatial distribution of targets and terrain based onusing a significantly reduced number of needed transmit-ted and/or received electromagnetic waveforms. This newscheme allows the aperture to be compressed and presentsmany new advantages which include strong resistance tocountermeasures and interception, imaging much widerswaths, and reduced on board storage constraints.

Glenn EasleySystems Planning Corporationgeasley@sysplan.com

Vishal Patel, Dennis Healy, Rama ChellappaUniversity of Marylandpvishalm@umd.edu, dhealy@umd.edu, rama@cfar.umd

CP7

Multiple Measurement Vector Problem withSubspace-Based Algorithm

In multiple measurement vector problem, we consider theproblem of the recovery of vectors which have commonsparsity patterns. First, when we have sufficient numberof measurements, we can recover the jointly sparse vectorswith a MUSIC-style algorithm. Then we propose a varia-tion of MUSIC-style subspace-based algorithm to recoverthe jointly sparse vectors efficiently when we have insuffi-cient number of random measurements or noisy measure-ments.

Jong Min Kim, Jong Chul YeKAISTfranzkim@gmail.com, jong.ye@kaist.ac.kr

CP7

Sparse and Fast Fourier Transforms in BiomedicalImaging

A straightforward discretization of high dimensional prob-lems often leads to a serious growth in the number of de-grees of freedom and thus even efficient algorithms like thefast Fourier transform have high computational costs. Uti-lizing sparsity allows for a severe decrease of the problemsize but asks for the customization of efficient algorithmsto these thinner discretization. We discuss modern gen-eralizations of the FFT and their application in emergingimaging modalities like photoacoustic tomography.

Stefan KunisChemnitz University of TechnologyFaculty of Mathematicskunis@mathematik.tu-chemnitz.de

CP7

Compressive Radar Imaging

In this article, far-field space-time radar imaging problems

IS10 Abstracts 49

are formulated in the framework of compressive sensing.The recoverability of detecting point scatterers, located ona lattice searching plane, is analyzed by the mutual coher-ence of the sensing matrix which is constructed from de-signing signal waveform and radar imaging formulation. Itis shown that the coherence of the sensing matrix is highlyrelated to the choice of the waveform, and the sensing po-sition due to the grid structure. Numerical experiments ofrecoverability by pursuits are also provided.

Hsiao-Chieh TsengDept. of Math, UCDavishctseng@math.ucdavis.edu

CP8

A New Variational Edge Representation for ImageSegmentation Using Active Contours

We consider an approach to segmentation motivated bythe Chan-Vese idea of minimizing a linear combinationof the pixel variances inside and outside a contour. Ourmethod maximizes the contrast between inside and out-side pixel averages relative to an adaptively defined inter-mediate value. The model is easier to configure the freeparameters than that of Chan-Vese while demonstratingthe efficiency and comparing the performances on a rangeof image data.

Alireza Aghasi, Bruce M. Boghosian, Eric MillerTufts Universityalireza.aghasi@tufts.edu, bruce.boghosian@tufts.edu,elmiller@ece.tufts.edu

CP8

Spectral Segmentation of Polygonized Images withNormalized Cuts

We present an implementation of the Normalized Cutsmethod adapted for spectral segmentation of polygonizedimages. We make novel observations regarding the effectsof the rounding errors on the Fiedler solution and othereigenvectros of the affinity matrix when computations arecarried out in finite precision. These observations motivateus to partition the image in the multidimensional spacespanned by the transposed matrix of the few of the lowesteigenvectors of the affinity matrix. We develop a new lowcomplexity implementation of the Mean Shift method inorder to produce meaningful and efficient clustering of thecomputed eigenvector subspace. We conduct a compara-tive study of the developed method with the MultiscaleNormalized Cuts and Segmentation by Weighted Aggre-gation methods that demonstrates comparable and evensuperior performance of the proposed method.

Anna Matsekh, Alexei SkurikhinLos Alamos National Laboratorymatsekh@lanl.gov, alexei@lanl.gov

Edward RostenUniversity of Cambridgeer258@cam.ac.uk

CP8

A Soft Segmentation Model Using Functionals withVariable Exponent

We propose here an efficient soft Mumford-Shah stochasticmodel for segmentation of a mixture patterns image. We

construct a functional with variable exponent which allowseach pixel to belong to each image pattern with differentprobability and combines the TV-based and isotropic diffu-sion. By taking different Gaussian means and variances oneach image pattern, the segmentation becomes more accu-rate. Numerical examples of natural and synthetic imagesare presented to illustrate the use of the model.

Iulia Posirca, Yunmei ChenUniversity of Floridaiuliap@math.ufl.edu, yun@math.ufl.edu

Celia A. BarcelosUniversidade Federal de UberlandiaUberlandia, MG - Brazilceliazb@ufu.br

CP8

Supervised Segmentation of Multi-Banded ImageData Using Statistically-Based Methods

Both spatial and non-spatial statistically-based classifica-tion methods are explored on the problem of segmentingimagery. For the learning step, in which training data isused to build the classifier, we use quadratic discriminantanalysis. Training data is obtained from the image we wishto classify using a MATLAB graphical user interface (GUI)created by us for this purpose. Post classification smooth-ing is implemented using nonlinear filtering, probabilitylabel relaxation, and Markov random fields.

Marylesa Wilde, John BardsleyThe University of Montanamarylesa.wilde@umontana.edu, bardsleyj@mso.umt.edu

Chris GotschalkUC Santa Barbaragots@lifesci.ucsb.edu

Mark LorangThe University of Montanamark.lorang@umontana.edu

CP8

Nonparametric Image Segmentation Using Renyi’sStatistical Dependence Measure

We present a novel nonparametric image segmentation ap-proach, which partitions an image by maximizing the sim-ilarity between that image and its label image. Renyi’sstatistical dependence measure, maximum cross correla-tion (MCC), is employed to measure the similarity. MCCdeals only with samples and does not need to estimate thecontinuous joint probability density function, which is sen-sitive to image quantization and makes the optimizationprocess complex. The computation is further simplified bythe theory of reproducing kernel Hilbert spaces.

Haili Zhang, Yunmei ChenDepartment of MathematicsUniversity of Floridahlzhang@ufl.edu, yun@ufl.edu

Jiangli ShiUniversity of Floridajianglishi@gmail.com

50 IS10 Abstracts

MS1

Distributed Compressive Imaging

We consider the problem of compressive imaging for dis-tributed imaging sensors. Distributed Compressive Imag-ing offers joint image compression/reconstruction fromimaging sensors which have overlapping fields-of-view.When viewed as a composite image sampling mechanism,a network of imaging sensors could transmit dramaticallyless data than current technologies while maintaining orsurpassing image reconstruction quality of the underlyingscene. We present performance results as a function of thenumber of cameras, transmission bandwidth, and cameraperspective registration accuracy.

Chris HuffDepartment of MathematicsUniversity of Central Floridachrishuffmath@gmail.com

MS1

CS Imaging Applications and Challenges

We developed an optical imaging technique based on com-pressive sensing. One area where we have implementedthis system is infrared imaging where the advantages in-clude lower costs and higher sensitivity. The same systemarchitecture is also employed in hyperspectral compressivesensing imaging with the potential to go directly from mea-surements to identification without the need to reconstructthe entire hyper cube. Lastly, a compressive sensing echellespectrometer has been also been built.

Kevin KellyElectrical and Computer Engineering DepartmentRice Universitykkelly@rice.edu

MS1

Compressive Imaging for Target Tracking

We consider the application of compressive imaging theoryto the problem of persistent surveillance. As compressivesensing enjoys significant research attention, applicationareas for compressive imaging are becoming clearer. Wehighlight several prospective compressive imaging applica-tions which could increase current performance by ordersof magnitude. Each application has algorithm and hard-ware implications which will be discussed. Specifically, wepresent expanded field-of-view imaging, expanded framerate video, exploitation while sensing, and multiplatformimage fusion.

Robert R. MuiseLockheed Martinrobert.r.muise@lmco.com

MS1

A Multiscale Framework for Compressive Sensingof Video

We consider the application of Compressive Sensing (CS)to video signals. In standard video compression, motioncompensation techniques have led to improved sparse rep-resentations; we adapt these techniques for CS recovery.Using a coarse-to-fine reconstruction algorithm, we alter-nate between motion estimation and motion-compensatedwavelet-domain signal recovery. Our algorithm allows therecovery of video sequences from fewer measurements than

either frame-by-frame or inter-frame difference recoverymethods.

Michael B. WakinDivision of EngineeringColorado School of Minesmwakin@mines.edu

MS2

Full Wave Equation Depth Extrapolation for Mi-gration

Using the full wave equation for depth wave-field extrapola-tion leads to an ill-posed problem. In avoiding the blow-upof evanescent waves, a typical downward extrapolation ina variable background uses approximate one-way propaga-tors and partially suppresses useful propagating waves, e.g.,generated by steep reflectors. Recently, we developed a newalgorithm for downward extrapolation which removes onlythe evanescent waves and leaves all propagating modes in-tact. Numerical experiments confirm significant improve-ments in seismic migration using our approach.

Gregory BeylkinUniv. of Colorado, Boulderbeylkin@boulder.colorado.edu

Kristian SandbergGeoEnergy, Corp.kristian@geoenergycorp.com

MS2

Imaging with Multiply Scattered Waves: Remov-ing Artifacts

The majority of seismic imaging assumes the single-scattering approximation, which linearizes the inverseproblem. When recorded data do not satisfy this assump-tion artifacts appear in the computed images. In specificmethods for imaging using multiply-scattered waves, singlyscattered waves produce similar artifacts in the resultingimages. We will discuss new techniques for estimating andremoving these artifacts in the context of one-way methodsfor seismic imaging.

Alison MalcolmMITamalcolm@mit.edu

Maarten de HoopCenter for Computational & Applied MathematicsPurdue Universitymdehoop@math.purdue.edu

Bjorn UrsinNorwegian University of Science and Technologybjorn.ursin@ntnu.no

MS2

Operator Upscaling for Seismic Inversion

While upscaling has been studied extensively for reservoirsimulation, its use for wave propagation is less common,despite the inherent multiscale character of the subsurface.Inversion studies typically rely on settling on a single scaleof interest in estimated material parameters. We investi-gate using a two-scale solution algorithm for the acousticwave equation as a forward simulator for inversion. The

IS10 Abstracts 51

two-scale algorithm parallelizes with almost no communi-cation and captures sub-wavelength heterogeneities on thecoarse scale.

Susan E. MinkoffUniversity of Maryland, Baltimore CountyDept of Mathematics and Statisticssminkoff@umbc.edu

MS2

Image Amplitudes in Wave Equation Imag-ing/inversion

Wave equation imaging often yields structurally correct im-ages of the Earth. However, it is more difficult to obtainthe correct amplitude for the structures in the image. HereI present recent progress in this problem. Topics will be (1)the estimation of position and direction dependent scalingfactors by which to correct image amplitudes, and (2) thecase of a single source, where we can derive a microlocalinverse.

Christiaan C. StolkUniversity of AmsterdamC.C.Stolk@uva.nl

MS3

Improved Dynamic PET via Kinetic Models andOperator Splitting

Dynamic Positron Emission Tomography allows monitor-ing physiological processes within the body that can bedescribed by kinetic parameters. However, recovery ofthese parameters often requires the solution of complex andnonlinear operator equations. Advanced operator split-ting techniques allow incorporating a-priori knowledge, e.g.sparsity of minimizers with respect to an exponential basis,into the reconstruction process.

Martin BenningInstitute for Computational and Applied MathematicsUniversity of Muenstermartin.benning@wwu.de

MS3

An Explicit Primal-Dual Algorithm for Large Non-Differentiable Convex Problems

In this talk, based on joint work with Xiaoqun Zhang andTony Chan, I will discuss a modification of the primal-dual hybrid gradient (PDHG) algorithm proposed by Zhuand Chan. The PDHG method applied to a saddle pointformulation of a convex minimization problem proceeds byalternating proximal steps that maximize and minimize pe-nalized forms of the saddle function. This can be useful forproducing explicit algorithms for large non-differentiableconvex problems, and a slight modification to the methodcan be made to guarantee convergence. For the problemof minimizing sums of convex functionals composed withlinear operators, I will show how to use operator splittingtechniques that allow the modified PDHG method to be ef-fectively applied. Specific applications to constrained TVdeblurring and compressive sensing problems will be pre-sented.

Ernie EsserUCLA Mathematics DepartmentUniversity of California Los Angelesernmon@math.ucla.edu

Xiaoqun ZhangUniversity of California Los Angeles.xqzhang@math.ucla.edu

Tony ChanUniversity of California. Los Angeleschan@math.ucla.edu

MS3

Subspace Correction Methods for �1 and TotalVariation Minimization

In the context of compressed sensing and sparse recovery,it has been clarified that the minimization of �1-norms oc-cupies a fundamental role for the promotion of sparse so-lutions. This understanding furnishes an important inter-pretation for total variation minimization, i.e., the mini-mization of the L1-norm of derivatives, as a regularizationtechnique for image restoration. These minimizations aretypically nonsmooth and are performed with algorithmswhose convergence is usually proved by compactness ar-guments; in particular there are no guaranteed rates ofconvergence in general. For very large scale problems se-quential algorithms fail to approximate minimal solutionsin acceptable computational time. Therefore it is desirableto consider domain decomposition or subspace correctionstrategies. In presence of nonsmooth convex constraintswhich are not splitting additively with respect to a decom-position, it is well known that such strategies will fail toconverge to minimizers in general. In this talk we presentseveral new results of convergence for domain decomposi-tion and subspace correction methods specifically tailoredfor �1-norm and total variation minimization. We will alsopresent counterexamples for situations where this strategyfails. We illustrate the theoretical results by presentingseveral numerical examples.

Massimo FornasierJohann Radon Institute for Computational and AppliedMathematics (RICAM)massimo.fornasier@oeaw.ac.at

MS3

Recent Numerical Methods for Large-scale Prob-lems in Imaging Applications

In this presentation I shall give an overview about recentadvances in the efficient numerical solution of total varia-tion minimization for large-scale imaging applications.

Carola-Bibiane SchonliebInstitute for Numerical and Applied MathematicsGeorg-August University of Goettingenc.schoenlieb@math.uni-goettingen.de

MS4

Diffeomorphic Image Registration using Gauss-Newton Optimisation

This work frames image registration in terms of estimat-ing MAP or regularised maximum likelihood solutions forthe deformations. Diffeomorphic deformations are param-eterised by their initial velocities, which are estimated viaa Gauss-Newton optimisation scheme. At each iteration,the coefficients parameterising the initial velocity are in-cremented by a matrix division of the first derivatives bythe (expectation of the) second derivatives. The solutionfor this division is obtained using a multigrid approach.

52 IS10 Abstracts

Images are assumed to consist of binary labelled regions,and the template encodes the mean of the multinomial dis-tributions from which the images are drawn. The templateis modelled by a Gaussian process (over 3D space) that is”squashed” using a softmax function.

John AshburnerWellcome Trust Centre for NeuroimagingFunctional Imaging Laboratoryjohn@fil.ion.ucl.ac.uk

MS4

Statistical Analysis of Neuroanatomy

A primary goal of Computational Anatomy is the statisti-cal analysis of anatomical variability. A natural questionthat arises is how does one define the image of an ”AverageAnatomy”. Such an ”average” must represent the intrin-sic geometric anatomical variability present. Large De-formation Diffeomorphic transformations have been shownto accommodate the geometric variability but performingstatistics of Diffeomorphic transformations remains a chal-lenge. In this lecture I will further extend this notion ofaveraging for studying change of anatomy on average froma cross sectional study of growth. Regression analysis isa powerful tool for the study of changes in a dependentvariable as a function of an independent regressor variable,and in particular it is applicable to the study of anatom-ical growth and shape change. When the underlying pro-cess can be modeled by parameters in a Euclidean space,classical regression techniques are applicable and have beenstudied extensively. However, recent work suggests that at-tempts to describe anatomical shapes using flat Euclideanspaces undermines our ability to represent natural biolog-ical variability. In this lecture I will develop a method forregression analysis of general, manifold-valued data. Fur-ther more I will extend the notion of Robust estimation toManifold valued data. The Median is a classic robust esti-mator of centrality for data. In this lecture I will formulatethe geometric median of data on a Riemannian manifold asthe minimizer of the sum of geodesic distances to the datapoints. I will exemplify the robustness of the estimationtechnique by applying the procedure to various manifoldscommonly used in the analysis of medical images. Usingthis approach, we also present a robust brain atlas estima-tion technique based on the geometric median in the spaceof deformable images.

Sarang JoshiScientific Computing and Imaging InstituteUniversity of Utahsjoshi@sci.utah.edu

MS4

Statistical Analysis of Image Warping Issues withM-estimation

A current trend is the study of probabilistic and statisti-cal aspects of deformation models, and the development ofconsistent statistical procedure for the estimation of tem-plate images. We consider a set of images randomly warpedfrom a mean template which has to be recovered. For this,we fisrt consider a semiparametric framework and showthat minimization a well-suited contrast can lead to effi-cient estimatots; then in a non parametric framework, un-der an appropriate statistical parametric model to generaterandom diffeomorphic deformations in two-dimensions, wefocus on the problem of estimating the mean pattern when

the images are observed with noise.

Jean-Michel LoubesEquipe de Statistique et Probabilites UMR 5219Universite de Toulouse 3, Institut de Mathematiquesloubes@math.univ-toulouse.fr

MS4

Statistical Analysis of Anisotropic Brownian ImageTextures

In this talk, I focus on the analysis of anisotropy in imagetextures. To deal mathematically with this issue, I presenta statistical framework gathering some anisotropic exten-sions of the fractional Brownian field. In this framework,I give several asymptotic results about the estimation ofmodel parameters and the testing of anisotropy. I alsopresent some applications to bone X-ray images and mam-mograms.

Frederic RichardMAP5 - UMR CNRS 8145University Paris Descartesfrederic.richard@parisdescartes.fr

MS5

A Variational Approach to Blind Image Deconvo-lution

Blind Image Deconvolution is a challenging problem onwhich much recent progress has been made. In my talkI will describe a regularization scheme based on image-gradient priors and explain its use in a variational frame-work. I will to explain why conventional MAP formula-tions yield degenerate solutions and how a variational ap-proaches can avoid them, enabling good quality results tobe recovered.

Rob FergusNew York Universityfergus@cs.nyu.edu

MS5

Variational Formulation for Nonlocal Image De-blurring with Collaborative l0-Norm Prior

Non-local patch-based estimation is currently one of themost promising directions in image processing. Within thisframework, a number algorithms has been developed fordifferent imaging problems and particularly for image de-noising, where the BM3D filters represent the state-of-the-art in terms of quality (Katkovnik et al., Int. J. ComputerVision, 86(1) 1-32, 2010). We recently proposed a specialprior which allows to reformulate the multistage BM3Dhard-thresholding as minimization of a global energy cri-terion (Katkovnik, TICSP Series 47, 305-319, 2009). Thisprior was further developed as a tool for the design of veryefficient deblurring algorithms in which the collaborativel0-norm penalty works as a spatially adaptive regulariza-tor (Katkovnik and Egiazarian, Proc. LNLA2009). Themain contribution presented in this talk concerns the de-velopment and testing of a frequency-domain recursive al-gorithm minimizing the collaborative nonlocal l0-norm cri-terion. Simulations demonstrate a very good performanceof the algorithm.

Vladimir Katkovnik, Karen EgiazarianTampere University of Technologyvladimir.katkovnik@tut.fi, karen.egiazarian@tut.fi

IS10 Abstracts 53

Alessandro FoiDepartment of Signal ProcessingTampere University of Technology, Finlandalessandro.foi@tut.fi

MS5

Optimizing the Blur-Noise Tradeoff with Multiple-Photo Capture

Capturing multiple photos at different focus settings isa powerful approach for reducing optical blur, but howmany photos should we capture within a fixed time bud-get? We develop a framework to analyze optimal cap-ture strategies balancing the tradeoff between defocus andsensor noise, incorporating uncertainty in resolving scenedepth. We derive analytic formulas for restoration errorand use Monte Carlo integration over depth to derive opti-mal capture strategies for different camera designs, undera wide range of photographic scenarios. We also derive anew upper bound on how well spatial frequencies can bepreserved over the depth of field. Our results show thatby capturing the optimal number of photos, a standardcamera can achieve performance at the level of more com-plex computational cameras, in all but the most demand-ing of cases. We also show that computational cameras,although specifically designed to improve one-shot perfor-mance, generally benefit from capturing multiple photos aswell. http://www.cs.toronto.edu/ hasinoff/timecon/

Sam HasinoffMITComputer Science and AI Labhasinoff@csail.mit.edu

Kiriakos KutulakosUniversity of TorontoComputer Sciencekyros@cs.toronto.edu

Fredo DurandMassachusetts Institute of Technologyfredo@mit.edu

William FreemanMITComputer Science and AI Labbillf@mit.edu

MS5

Deblurring with Advanced Optimization

We present a deblurring method using advanced optimiza-tion to alternate between blur kernel estimation and un-blurred image restoration. We present an analysis of thecauses of common artifacts found in current deblurringmethods, and then introduce several terms that are use-ful in deblurring. These terms include a model of thespatial randomness of noise in the blurred image, as wella local smoothness prior that reduces ringing artifacts byconstraining contrast in the unblurred image wherever theblurred image exhibits low contrast. Finally, we describean efficient optimization scheme.

Leo Jiaya JiaThe Chinese University of Hong Kongleojia@cse.cuhk.edu.hk

Qi Shan

Washington Universityshanqi@cs.washington.edu

Aseem AgarwalaAdobe Systemsaseem@agarwala.org

MS5

Superresolution and Blind Deconvolution of Video

In many real applications, traditional superresolutionmethods fail to provide high-resolution images due to ob-jectionable blur and inaccurate registration of input low-resolution images. In this talk, we present a method of su-perresolution and blind deconvolution of video sequencesand address problems of misregistration, local motion andchange of illumination. The method processes the video byapplying temporal windows, masking out regions of mis-registration, and minimizing a regularized energy functionwith respect to the high-resolution frame and blurs, whereregularization is carried out in both the image and blurdomains. Experiments on real video sequences illustraterobustness of the method.

Filip Sroubek, Jan FlusserCzech Academy of Sciencessroubekf@utia.cas.cz, flusser@utia.cz

MS6

Impact of JPEG Compression and Resolution De-creasing in Stereo Accuracy

In this work, we quantitatively study the impact of JPEGcompression in stereo accuracy. We compare this accu-racy with the one obtained by a convolution+subsamplingcompression strategy. We show that for the same rate ofcompression a better accuracy is obtained by this latterstrategy.

Bartomeu CollUniversitat Illes Balearstomeu.coll@uib.es

Antoni BuadesParis Descartestoni.buades@uib.es

Jean-Michel Morel, Bernard RougeENS Cachanmorel@cmla.ens-cachan.fr, rougebe@free.fr

MS6

Variational Methods Stereo and Multi-view Recon-struction

I will address the shape optimization challenges in stereoand multiview reconstruction by means of variationalmethods. I will show that multiple view reconstructionand stereo depth estimation can be solved by minimizingconvex functionals over convex domains. This allows tocompute globally optimal solutions which are independentof initialization and of the choice of minimization strat-egy. Furthermore, I will present the first super-resolutionalgorithm for texture estimation in the multiview context.

Daniel Cremers, Kalin Kolev, Bastian GoldlueckeDepartment of Computer Science

54 IS10 Abstracts

University of Bonndcremers@cs.uni-bonn.de, kolev@cs.uni-bonn.de,bastian@cs.uni-bonn.de

Thomas PockInstitute for Computer Graphics and VisionGraz University of Technologypock@icg.tugraz.at

MS6

A Contrario Image Matching: Shape-elements,Shape-Context, SIFT, PCA

In image matching problems we are confronted to decidewhether two descriptors are alike or not. In situationswhere a model of the structure to be detected cannot be es-timated, the a-contrario methodology based on controlingthe number of false alarms (NFA) leads automatic detec-tion thresholds. In this talk we present a general techniqueto obtain accurate estimates of the NFA, and its applica-tion to secure matches of image level lines, patches, SIFTor Shape-Context.

Pablo MuseFacultad de Ingeniera - Universidad de la RepblicaUruguaypmuse@fing.edu.uy

MS6

Optimal Stereo Matching Reaches Theoretical Ac-curacy Bounds

This talk will focus on accuracy in block-matching forstereo-rectified images and how the disparity map can becomputed for a majority of image points up to a 1/20 pixelprecision. A theoretical prediction of the errors caused bynoise will be given, and it will be proved on several simu-lated and real experiments that this bound is reached bythe proposed algorithm. Experiments on the Middleburybenchmark show that the presented method improves theprecision of the ground truth.

Neus SabaterCMLA - ENS CachanFranceneussabater@gmail.com

Andres AlmansaTelecom ParisTech & CNRSalmansa@enst.fr

Jean-Michel MorelENS Cachanmorel@cmla.ens-cachan.fr

MS7

Estimating Suitable Metrics for an Empirical Man-ifold of Shapes

We propose a framework to learn shape metrics from a setof examples of shapes, able to handle sparse sets of highlyvarying shapes, like human silhouettes. The tangent spaceof a shape being the set of all infinitesimal deformationsthat can be applied to it, an inner product in a tangentspace can be seen as a deformation prior, and thus as aGaussian distribution. We formulate the task of finding theoptimal metrics, i.e. the inner products in tangent spaceswhich suit the best a given empirical manifold of shapes, as

a classical minimization problem. The energy to be min-imized involves the inner product cost of observed localdeformations (reliable matchings between close shapes) aswell as a regularization term based on transport of defor-mations and Kullback-Leibler divergence. Surprisingly, theglobal minimum of this functional on metrics is related toprincipal component analyses and is easy to compute.

Guillaume CharpiatPULSAR team - INRIAguillaume.charpiat@sophia.inria.fr

MS7

Spatiotemporal Atlas Building via Frechet Meansof Diffeomorphisms

The construction of average models of anatomy, as well asregression analysis of anatomical structures, are key issuesin medical research, e.g., in the study of brain develop-ment and disease progression. However, anatomical shapechange is often modeled using transformations—such asthe group of diffeomorphisms—that do not form a linearspace. This talk describes methods for defining averagesand kernel-based regression for anatomical structures viathe Frechet mean and a diffeomorphism-based metric.

Brad DavisKitware. Inc.brad.davis@kitware.com

MS7

Conformal and Multi-scale Metrics on ShapeSpaces

We will present several families of metrics on curves andsurfaces, each of which is based on some multi-scale repre-sentation and is equivalent to a Sobolev-type norm. Thesemetrics measure local regularity of a curve or surface, withexplicit recognition of the role played by scale. We willpresent both theoretical and experimental results.

Matt FeiszliYale, Mathematicsmatt.feiszli@yale.edu

MS7

A Computable Formulation of Curvature for theRiemannian Manifold of Landmarks

In the past few years there has been a growing interest, indiverse scientific communities, in endowing ”shape spaces”with Riemannian metrics, so to be able to measure simi-larities between shapes and perform statistical analysis ondata sets (e.g. for object recognition, target detection andtracking, classification, and automated medical diagnos-tics). The geometry of such spaces has started to emergeonly very recently; in this talk we will explore the sec-tional curvature for the Riemannian manifold of landmarkpoints (which is one of the simplest, in that it is finite-dimensional) and discuss its effects on applications.

Mario MicheliUCLA– Mathematicsmicheli@math.ucla.edu

MS8

Fast Sensitivity Encoding with Arbitrary k-space

IS10 Abstracts 55

Trajectories in Partial Parallel Imaging

Speed is a crucial issue in MR imaging in many clinicalapplications. This paper presents a fast reconstructionalgorithm of Sensitivity Encoding with arbitrary k-spacetrajectories to improve the clinical applicability of partialparallel imaging (PPI). The proposed method combines thevariable-splitting and quadratic penalty techniques in op-timizations with an accelerated gradient method. By us-ing variable-splitting and penalty techniques the originalmodel can be reformulated as an unconstrained minimiza-tion problem, whose minimizers can be computed by solv-ing a TV denoising problem and a linear inverse problemseparately and iteratively. TV denoising problem can besolved efficiently by several re cently developed numericalmethods. While due to the nature of PPI the inverse prob-lem can be ill-conditioned to a degree that increases withreduction factor in data acquisition. This makes the inver-sion much more unstable and time consuming. To over-come this difficulty an optimal first order gradient methodin the sense of complexity analysis developed by Nesterovis applied in our scheme. M oreover, a gridding preprocess,that shifts the non-Cartesian data onto Cartesian grids, isused to avoid the inverse gridding in each iteration for fur-ther reduction of computational time. Comparisons withvarious recently proposed methods indicate the outstand-ing efficiency of our algorithm with state-of-the-art recon-struction effects.

Xiaojing YeDepartment of Mathematics, University of Florida358 Little Hall, Gainesville, FL32611-8105xye@ufl.edu

Yunmei ChenUniversity of Floridayun@math.ufl.edu

Feng HuangInvivo Corporation, Philips HealthCare, Gainesville, FLf.huang@philips.com

MS8

Variational Properties of a Functional for Multi-phase Segmentation

We consider a functional for multiphase image segmen-tation which has been proposed by Sandberg, Kang andChan. The functional is a modified version of the Mum-ford and Shah functional for the partition problem. In thenew functional the length term of the Mumford and Shahfunctional is multiplied by the sum of the ratios perime-ter/area of the sets of the partition. We prove the existenceof minimizers for a weak version of the functional definedon the class of sets with finite perimeter. Then we studythe regularity of boundaries of sets which constitute a weakminimizer. Technical tools used in the proofs are adaptedfrom the analysis of the Mumford and Shah functional inthe piecewise constant case.

Riccardo MarchIstituto per le Applicazioni del Calcolo, CNRr.march@iac.cnr.it

Sung Ha KangGeorgia Inst. of TechnologyMathematicskang@math.gatech.edu

MS8

Efficient Global Optimization for the MultiphaseChan-Vese Model of Image Segmentation by GraphCuts

The Mumford-Shah model is an important variational im-age segmentation model. A popular multiphase level setapproach, the Chan-Vese model, was developed for thismodel by representing the phases by several overlappinglevel set functions. Recently, binary level set functionswere proposed as a variant representation of the Chan-Vesemodel. In both approaches, the gradient descent equationshad to be solved numerically, a procedure which is slowand has the potential of getting stuck in a local minima.In this work, we develop an ecient and global minimizationmethod for the binary level set representation of multi-phase Chan-Vese model based on graph cuts. If the av-erage intensity values of the dierent phases are sucientlyevenly distributed, the energy function becomes submod-ular. Otherwise, a novel method for minimizing nonsub-modular functions is proposed with particular emphasis onthis energy function. We also show that non-local exten-sions of the multiphase Chan-Vese model can be globallyminimized by our method.

Egil BaeUniversity of Bergenegil.bae@math.uib.no

Xue-cheng TaiDept. of Mathematics, University of Bergen, Norway andDiv. of Math. Sciences, Nanyang Tech. Universitytai@mi.uib.no

MS8

Dual Norm Based Iterative Methods for ImageRestoration

Proximal point methods have been employed to stabilizeill-posed problems in the last decades (see Osher et al.,He et al.) which employ L2-quadratic and L1 data-fittingterms, respectively. Recently, Iusem-Resmerita proposeda proximal point method for minimizing a convex func-tion defined on a non-reflexive Banach space which is thedual of another Banach space. Our aim here is to investi-gate, based on that method, several approaches to imagerestoration.

Miyoun JungDepartment of MathematicsUCLAgomtaeng@math.ucla.edu

Elena ResmeritaIndustrial Mathematics InstituteJohannes Kepler Universityelena@ricam.oeaw.ac.at

Luminita A. VeseUniversity of California, Los AngelesDepartment of Mathematicslvese@math.ucla.edu

MS8

Mean Curvature Based Image Denoising

We propose a new variational model for image denoising,which employs mean curvature information of the imagesurface (x, f(x)) induced by the given image f : Ω → R.

56 IS10 Abstracts

Besides eliminating noise and preserving edges of objectsefficiently, our method can keep corners of objects andgrey-scale intensity contrasts of images, and also removethe staircase effect. We apply the proposed model for thedenoising of curves and plane images, and also comparethe results with those by using the classical Rudin-Osher-Fatemi model.

Wei ZhuMathematics, University of Alabamawzhu7@bama.ua.edu

MS9

Imaging and Time Reversal in Scattering Environ-ments

This minitutorial will provide an introduction to sensor ar-ray imaging in cluttered media. We will analyze how wavescattering by the inhomogeneities of the medium can af-fect the resolution and the signal-to-noise ratio in imagingan object from far-field measurements. We will show hownovel image-enhancement techniques have been obtainedusing tools from statistics and wave propagation in ran-dom media. We will clarify the relations between timereversal experiments, active sensor imaging using migra-tion or backpropagation of the array data set, and passivesensor imaging using cross correlations of ambient noisesignals.

Josselin GarnierUniversite Paris 7garnier@math.jussieu.fr

MS10

Methods for Confocal Microscpic 3D ImageRestoration

We propose methods for the iterative restoration of fluores-cence Confocal Laser Scanning Microscope (CLSM) imageswhich are degraded by both blur and Poisson noise. Therestoration is obtained as the minimization of the sum of adata term (given by the Poisson distribution) and a priorterm, which is a TV prior term, or a complex wavelet L1norm. We investigated two possibilities: a criterion writtenin the image domain (analysis case) or in the wavelet do-main (synthesis case) . Results will be shown on biological3D images.

Laure Blanc-Feraud, Praveen Pankajakshan, MikaelCarlavan, Josiane ZerubiaINRIASophia Antipolis, Francelaure.blanc feraud@sophia.inria.fr, xxx, xxx, xxx

Jean-Christophe Olivo-MarinInstitut Pasteur, Paris, Francexxx

MS10

Multilevel Algorithm for a Poisson Noise RemovalModel with Total-Variation Regularization

Many commonly used models for the fundamental imageprocessing task of noise removal can deal with Gaussianwhite noise. However such Gaussian models are not effec-tive to restore images with Poisson noise, which is ubiqui-tous in certain applications. Recently Le-Chartrand-Asakiderived a new data-fitting term in the variational model for

Poisson noise. This paper proposes a multilevel algorithmfor efficiently solving this variational model. As expectedof a multilevel method, it delivers the same numerical so-lution many orders of magnitude faster than the standardsingle-level method of coordinate descent time-marching.Supporting numerical experiments on 2D gray scale imagesare presented.

Raymond H. ChanThe Chinese Univ of Hong KongDepartment of Mathematicsrchan@math.cuhk.edu.hk

Ke ChenUniversity of LiverpoolLiverpool, UKrchan@math.cuhk.edu.hk

MS10

Fast Bayesian Reconstruction For Fully-3DPositron Emission Tomography

3D Positron Emission Tomography is an ill-posed inverseproblem that can be solved by penalized likelihood opti-mization, to account for both noise and object statistics.However, solving such a large-scale, space-variant problemremains a computational challenge. Our contribution is anew approximation of the Hessian of the Poisson likelihood,which yields a substantial acceleration of inexact Newtonalgorithms. It also facilitates the prior weights tuning toproduce a reconstructed image with uniform and isotropicspatial resolution.

Xavier RondeauIRCCYN, Nantes (FRANCE)CRAL, CNRS, Saint-Genis-Laval (FRANCE)xavier.rondeau@irccyn.ec-nantes.fr

Jerome IdierIRCCYNNantes, Francexxx

Claude ComtatCEAOrsay, Francexxx

Eric ThiebautCNRSSaint-Genis-Laval, Francexxx

MS10

Total Variation Processing of Images with PoissonStatistics

This talk deals with denoising of density images with poorPoisson statistics. We propose total variation (TV) basedregularization techniques adapted to the case of Poissondata, which we derive from approximations of logarith-mic a-posteriori probabilities. In order to guarantee sharpedges we avoid the smoothing of TV and use a dual ap-proach for the numerical solution. We illustrate the feasi-bility of our approaches for the reconstructions of cardiacdata in positron emission tomography.

Alex SawatzkyUniversity of Muenster

IS10 Abstracts 57

Muenster, Germanyalex.sawatzky@wwu.de

Christoph BruneInstitute for Computational and Applied MathematicsUniversity of Muenster, Germanychristoph.brune@wwu.de

Jahn Mueller, Martin BurgerUniversity of MuensterMuenster, Germanyjahn.mueller@wwu.de, martin.burger@wwu.de

MS11

Diffusion Generated Motion for Evolving Interfacesin Imaging and Vision

I will describe a class of algorithms for generating a va-riety of geometric motions of curves in 2D and surfacesin 3D. These algorithms reduce the desired geometric mo-tion to alternating two very simple operations for whichfast algorithms already exist: Convolution with a kernel,and construction of the signed distance function to a set.In particular, the resulting algorithms are unconditionallystable, allowing for arbitrarily large time steps constrainedonly by accuracy considerations. Applications include im-age segmentation and high order models in image inpaint-ing, as well as certain problems of materials science thatinvolve multiphase flow.

Selim EsedogluDepartment of MathematicsUniversity of Michiganesedoglu@umich.edu

MS11

A Multilevel Decomposition Method for Fast L1Regularized Deconvolution

Abstract not available at time of publication.

Tom GoldsteinUCLA Department of Mathematicstagoldst@math.ucla.edu

MS11

A Nonlinear PDE-based Method for Sparse Decon-volution

In this paper, we introduce a new nonlinear evolution par-tial differential equation for sparse deconvolution problems.We show that our PDE preserves the l1 norm while low-ering the measurement residual. More importantly the so-lution of the PDE becomes sparser asymptotically. There-fore, it can be treated as a natural and helpful plug-in tosome algorithms for l1 minimization problems, e.g. Breg-man iterative methods introduced to sparse reconstructionproblems.

Yu MaoUCLA Department of Mathematicsdavid.y.mao@gmail.com

Bin DongUCSDb1dong@math.ucsd.edu

Stanley J. Osher

University of CaliforniaDepartment of Mathematicssjo@math.ucla.edu

MS11

Tensor-valued Image Processing Using SplittingMethods

Tensor-valued data have gained significant importance inrecent years, e.g., in diffusion tensor magnetic resonanceimaging. Our aim is to transfer successful variational tech-niques for the restoration of scalar-valued images to thetensor-valued setting. We propose an operator-based ap-proach which makes use of the trace norm of matrices.Furthermore, we combine different regularizers includinghigher-order terms via the infimal convolution functional.Interestingly, the alternating split Bregman or Douglas-Rachford splitting method can be used to decouple theseregularizers. This gives rise to an efficient minimizationalgorithm.

Simon SetzerUniversity of Mannheimssetzer@kiwi.math.uni-mannheim.de

MS12

Patch-based Fluorescence Video-microscopy ImageRestoration

The noise represents one of the main limiting factor forthe spatial and temporal resolution of live fluorescence mi-croscopy. We present here an approach to reduce the noiselevel and improve the spatial resolution of the images. Fol-lowing the work of Kindermann and Osher (2005), we pro-pose to minimize a non-local patch-based functional to de-rive a point estimate. The performances of the estimatorare then improved by adapting its parameters using a bias-variance trade-off criterion.

Jerome BoulangerRICAM Linzjerome.boulanger@oeaw.ac.at

Peter ElbauRICAMpeter.elbau@oeaw.ac.at

MS12

4D Image Reconstruction via Optimal Transport

We discuss models and efficient algorithms for 4D recon-struction in photonic imaging. Standard reconstructionmethods do not incorporate time dependent information orkinetics. This can lead to deficient accuracy particularly atobject boundaries, e.g. at cardiac walls. We present jointmodels combining Poisson-TV reconstruction and conceptsof optimal transport (mass conservation). The numericalrealization is based on operator splitting techniques andUzawa methods. Dynamic deconvolution and PET resultsillustrate the performance of the proposed methods.

Christoph BruneInstitute for Computational and Applied MathematicsUniversity of Muenster, Germanychristoph.brune@wwu.de

58 IS10 Abstracts

MS12

Statistical Multi-scale Strategies for Inverse Prob-lems

In this talk, we present a novel class of statistical multi-resolution (SMR) estimators for statistical linear inverseproblems in Hilbert spaces. These SMR-estimators can becomputed in a completely data-driven way. We discussconsistency and convergence rates results in a very generalsetting. In particular, we consider deconvolution problemsin biophotonic imaging and show that our estimators canbe designed in order to control the trade-off between regu-larization and fit-to-data in a locally-adaptive way. Exam-ples from fluorescence microscopy illustrate our approach.

Klaus FrickUniversity of Gottingenfrick@math.uni-goettingen.de

MS12

Statistical Issues from Single-molecule Biophysics

Recent advances in nanotechnology allow scientists for thefirst time to follow a biological process on a single moleculebasis. These advances also raise many challenging sta-tistical inference problems. First, on the single-moleculelevel, by the law of statistical and quantum mechanics,the dynamics/process of a biomolecule is stochastic. Sec-ond, since the experiments focus on and study only afew molecules, the data in single-molecule experiments aremuch noisier than those in the traditional ensemble exper-iments in that one cannot use the actions of thousands ofmolecules to average out the noise. Third, inferring the un-derlying stochastic dynamics is usually complicated by thepresence of latent processes. In this talk we will use the in-ference of DNA hairpin kinetics to illustrate the statisticaland probabilistic challenges in single-molecule biophysics,and introduce a Bayesian data augmentation method toaddress the inference difficulties.

Samuel KouDept of StatisticsHarvard Universitykou@stat.harvard.edu

MS13

Numerical Resolution of Variational Problems In-volving Geodesic Distances

Various problems in imaging require to find metric thatminimizes under some constraints the geodesic lengths be-tween points. In this talk, I will present the SubgradientMarching Algorithm that computes a sub-gradient of a dis-cretized geodesic distance. It allows one to solve numer-icaly by projected sub-gradient descent variational prob-lems involving geodesic distances. I will show applicationto traffic congestion, landscape optimization and traveltime tomography in seismic imaging. This is a joint workwith Fethallah Benmansour, Guillaume Carlier and FilippoSantambrogio.

Fethallah BenmansourCEREMADE, Universite Paris Dauphinebenmansour@ceremade.dauphine.fr

Gabriel PeyreCeremade, Universite Paris Dauphinegabriel.peyre@ceremade.dauphine.fr

MS13

Fast High-Dimensional Data Clustering with TotalVariation

In this talk, I will introduce an algorithm for graph clus-tering. Graph clustering aims at grouping similar high-dimensional data s.a. images. The main problem of graphclustering is to minimize the cut of a graph. Popular cutsare the normalized cut of Shi-Malik (3000 citations) andthe Cheeger’s cut, which are NP-hard problems. We intro-duce a continuous relaxation of the Cheeger’s cut problemand we show that the relaxation is actually equivalent tothe original problem, which is not the case with the Shi-Malik’s relaxation. We also give an algorithm which is ex-perimentally very efficient on some clustering benchmarkssince the algorithm can cluster 10,000 high-dimensionalpoints in a few seconds. This is joint work with A. Szlam(NYU), T.F. Chan, T. Goldstein, and S. Osher (UCLA)

Xavier BressonUCLADepartment of Mathematicsxbresson@math.ucla.edu

MS13

Convex Relaxation Methods for Multilabel Opti-mization

In my presentation, I will introduce convex relaxationmethods to solve minimal parition problems and relatedmulti-label optimization problems. In contrast to com-monly employed level set methods, the proposed algo-rithms do not require an initialization. Moreover the solu-tions are either globally optimal or within a per-instancebound of the optimum. Furthermore I will present noveland provably convergent algorithms which allow to effi-ciently compute minimizers of the convex problems bymeans of projected gradient descent /ascent strategies.The class of functionals considered includes the piecewiseconstant and piecewise smooth Mumford-Shah functional.

This is joint work with Thomas Pock and Antonin Cham-bolle.

Daniel CremersDepartment of Computer ScienceUniversity of Bonndcremers@cs.uni-bonn.de

MS13

Using Mathematical Morphology to (Approxi-mately) Solve the TVL1 Model

Since the seminal work by Rudin-Osher-Fatemi in 1992,total variation models have become very popular. For thelast 10 years, the understanding of the behavior of the to-tal variation denoising models used in image processinghas dramatically improved, as a consequence of the worksof W. K. Allard, G. Belletini, V. Caselles, A. Chambolle,S. Esedoglu, M. Novaga, and others... Using tools de-veloped in these works, we will describe the geometricalbehavior of the TVL1 model and its connection with theCheeger problem. In the convex case, exact solutions ofthe TVL1 problem are given by an opening followed by asimple test over the ratio perimeter/area. Shapes remainor suddenly vanish depending on this test. This particu-lar behavior has allowed us to design an efficient numericalscheme based on morphological operators to simulate theTVL1 model. This work has been supported by the French”Agence Nationale de la Recherche” (ANR), under grants

IS10 Abstracts 59

NATIMAGES (ANR-08-EMER-009) ”Adaptivity for nat-ural images and texture representations” and FREEDOM(ANR07-JCJC-0048-01),”Movies, restoration and missingdata”.

Vincent DuvalTelecom ParisTechvincent.duval@telecom-paristech.fr

MS14

Image Processing with Higher-order Statistics onGrassmannians

We identify a subspace, i.e. a point on a Grassmannian,that best describes a collection of images by simultaneouslyaccounting for variation in cumulants of all orders. Forcomparison, PCA-based techniques (e.g. Eigenfaces andFisherfaces) take into account only the second order cumu-lant, i.e. covariance. While ICA-based techniques do usehigher-order cumulants, they invariably make strong as-sumptions on the higher-order cumulants (e.g. E[XYZ]=0).We try to model such irreducible higher-order dependencerather than assuming it is zero. A limited-memory quasi-Newton method on Grassmannian is used to perform therequisite optimization.

Lek-Heng LimUniversity of California at Berkeleylekheng@math.berkeley.edu

MS14

Multi-manifold Semi-supervised Learning

Semi-supervised learning on a single manifold has been thesubject of intense study. I will discuss the setting of multi-ple manifolds, in which it is assumed that the target func-tion is smooth with respect to the geodesic distance on eachmanifold, and the manifolds can intersect or partly over-lap. I will discuss a semi-supervised learning algorithmthat separates different manifolds into decision sets, andperforms supervised learning within each set. Using a fi-nite sample analysis, it is possible to quantify the potentialgain of using unlabeled data in this multi-manifold setting.I will also present a practical version of the algorithm thatinvolves a novel application of Hellinger distance and size-constrained spectral clustering.

Aarti SinghMachine Learning DepartmentCarnegie Mellon Universityaartisingh@cmu.edu

MS14

Hybrid Linear Modeling by Multiscale GeometricAnalysis

The hybrid linear modeling problem is to identify a set of d-dimensional affine sets in a D-dimensional Euclidean space.It arises, for example, in object tracking and structure frommotion. The hybrid linear model can be considered as thesecond simplest (behind linear) manifold model of data. Inthis paper we will present a very simple geometric methodfor hybrid linear modeling based on selecting a set of localbest fit flats that minimize a global l1 error measure. Thesize of the local neighborhoods is determined automaticallyusing Jones’ l2 beta numbers; it is proven under certain ge-ometric conditions that good local neighborhoods exist andare found by our method. We give extensive experimentalevidence demonstrating the state of the art accuracy and

speed of the algorithm on synthetic and real hybrid lineardata.

Arthur SzlamDepartment of MathematicsNYUaszlam@courant.nyu.edu

MS14

Robust Recovery of Low-Rank Structure from Im-agery Data

Principal component analysis is a fundamental operationin computational data analysis, with myriad applicationsranging from web search to bioinformatics to computer vi-sion and image analysis. However, its performance andapplicability in real scenarios are limited by a lack of ro-bustness to outlying or corrupted observations. This prob-lem can be formally stated as one of recovering a low rankmatrix from large but sparse corruption. In this talk, wediscuss recent progress on this problem. Recent theoreticalresults show that under fairly broad circumstances it canbe exactly and efficiently solved by convex programming.We discuss fast and scalable solutions to this convex pro-gram, via proximal gradient algorithms as well as duality.We then show how these new tools impact real imaging ap-plications, including automatic face recognition and opticflow estimation from video. These applications show thepower of the tools, but also demand non-trivial extensionsto nonlinear and manifold structure (e.g., due to transfor-mations of domain).

John WrightDepartment of Electrical and Computer EngineeringUniversity of Illinois at Urbana-Champaignjnwright@uiuc.edu

MS15

Fast Algorithms for Large-scale Diffusion-typeImaging Problems

In this work, we address a 2d tomography problem, wherewe try to reconstruct the absorption coefficient of an ellip-tic PDE from boundary measurements induced by a largenumber of sources. We consider a square geometry wherethe light sources and measurements are located regularlyon opposite sides of the domain. The problem in this formrequires solving a large nonlinear inverse problem, wherethe forward problem is given by multiple elliptic PDEs,and is thus computationally intensive. To address this,we propose to solve a linearized version of the problembased on the Born approximation and show that substan-tial gains can be made in computation. By revealing thespecial structure of the problem, we design fast methods toassemble the coefficient matrix for the linearized problem.We also propose fast matrix-vector product routines thatcan be used to solve the linear system with iterative meth-ods or sparse SVD. Finally we introduce a fast inversionalgorithm that produces the solution of the inverse problemby solving a sequence of small systems. We demonstratethe effectiveness of our method with several examples.

Gunay DoganMathematical and Computational Sciences DivisionNational Institute of Standards and Technologygunay.dogan@nist.gov

George BirosGeorgia Institute of Technology

60 IS10 Abstracts

biros@gatech.edu

MS15

Regularizing Kaczmarz Iterations: Analysis andApplication to Photoacoustic Tomography

We analyze regularizing Kaczmarz methods for solving sys-tems of linear ill-posed equations

Aix = yi for i = 0, . . . , N − 1 ,

which use each of the equations separately. Here Ai areoperators between spaces X and Yi. We are mainly inter-ested in the case where we have only noisy data yδ

i ∈ Yi

satisfying ‖yδi −yi‖ ≤ δi with δi > 0 (noise levels). Numer-

ical experiments are presented related to inverse problemsin photoacoustic tomography.

Markus HaltmeierCompational Science CenterUniversity of Viennamarkus.haltmeier@univie.ac.at

Otmar ScherzerComputational Science CenterUniversity Viennaotmar.scherzer@univie.ac.at

MS15

Multiphase Image Segmentation and ModulationRecovery Based on Shape and Topological Sensi-tivity

Topological sensitivity analysis is performed for the piece-wise constant Mumford-Shah functional. Topological andshape derivatives are combined in order to derive an algo-rithm for image segmentation with fully automatized ini-tialization. Segmentation of 2D and 3D data is presented.Further, a generalized Mumford-Shah functional is pro-posed and numerically investigated for the segmentationof images modulated due to, e.g., coil sensitivities.

Michael HintermuellerHumboldt-University of Berlinhint@math.hu-berlin.de

Antoine LaurainKarl-Franzens University of Graz, Austriaantoine.laurain@uni-graz.at

MS15

A Mumford-Shah Level-set Approach for Tomog-raphy Data - Reconstruction and Regularization

We deal with a level-set based approach for the simulta-neous reconstruction and segmentation of density and/oractivity distributions from tomography data. SPECT/CTis a hybrid imaging technique enabling a direct correlationof anatomical information (density distribution) from CT(Computerized Tomography) and functional information(activity distribution) from SPECT (Single Photon Emis-sion Computerized Tomography). We model activity anddensity distributions as piecewise constant functions. Thesegmenting contours and the corresponding function val-ues of both the activity and the density distribution arefound simultaneously as minimizers of a Mumford-Shahlike functional over the set of admissible contours and forfixed contours over the spaces of piecewise constant den-sity and activity distributions which may be discontinuous

across their corresponding contours. For the latter stepwe use a Newton method to solve the nonlinear optimalitysystem. We use shape sensitivity calculus to find a de-scent direction for the cost functional with respect to thegeometrical variable which leads to an update formula forthe contours in the level-set framework. The identificationof density and/or activity distributions from tomographydata is an ill-posed problem. After introducing a propernotion of convergence for the space of piecewise constantfunctions, we present results on the existence and conver-gence of minimizers for the Mumford-Shah like functionalfor linear operators. We present reconstructions from syn-thetic SPECT/CT data with different noise levels as wellas regularization theory for the Mumford-Shah like methodfor linear operators.

Esther KlannUniversity of Linz, Austriaesther.klann@ricam.oeaw.ac.at

Ronny RamlauJohannes Kepler Universitat Linz, Austriaronny.ramlau@jku.at

Wolfgang RingInstitut fuer MathematikUniversitaet Grazwolfgang.ring@kfunigraz.ac.at

MS16

Model Based Compressive Imaging

Compressive sensing is an alternative to Shannon samplingfor acquisition of sparse or compressible signals that canbe well approximated by just K ¡¡ N elements from an N-dimensional basis. The standard CS theory dictates thatrobust signal recovery is possible from M = O(K log(N/K))measurements. We demonstrate that it is possible to sub-stantially decrease M without sacrificing robustness byleveraging more realistic signal models that go beyond sim-ple sparsity by including dependencies between values andlocations of the signal coefficients.

Richard G. BaraniukRice UniversityElectrical and Computer Engineering Departmentrichb@rice.edu

MS16

A Fast Reconstruction Algorithm for DeterministicCompressive Sensing

We propose a deterministic compressed sensing matrix thatcomes by design with a very fast reconstruction algorithm,in the sense that its complexity depends only on the num-ber of measurements n and not on the signal dimensionN. The matrix construction is based on the second orderReed-Muller codes. This matrix does not have RIP uni-formly with respect to all k-sparse vectors, but it acts as anear isometry with very high probability.

Robert CalderbankPrinceton Universitycalderbk@math.princeton.edu

IS10 Abstracts 61

MS16

Compressive Sensing on Manifolds

Nonparametric Bayesian methods are employed to consti-tute a mixture of low-rank Gaussians, for high dimensionaldata constrained to a low-dimensional subregion. Thenumber of mixture components and rank are inferred fromthe data. The resulting algorithm can be used for learn-ing manifolds and reconstructing signals from manifolds,based on compressive sensing (CS) projection measure-ments. The statistical CS inversion is performed analyt-ically. We derive the required number of CS measurementsneeded for successful reconstruction.

Larry CarinElectrical & Computer EngineeringDuke Universitylcarin@ee.duke.edu

MS16

Sparse Learning via Iterative Minimization

We present a regularized approach to sparse signal recov-ery. Sparse Learning via Iterative Minimization, or SLIM,follows an lq-norm constraint (for 0 ¡ q = 1), and can thusbe used to provide increased sparsity compared to exist-ing l1-norm based approaches. We compare SLIM to sev-eral well-known sparse methods, including the widely-usedCoSaMP approach. Without significantly increasing com-putational cost, as compared to CoSaMP, we show thatSLIM provides superior performance for sparse signal re-covery applications.

Jian LiUniversity of Floridali@dsp.ufl.edu

MS17

Non-Additive Noise Removal Using Variable Split-ting and Augmented Lagrangian Optimization

We propose a new approach to handle non-additive noisemodels (namely multiplicative and Poissonian) in imagerecovery problems. Our approach uses two main buildingblocks: variable splitting, yielding a constrained optimiza-tion problem; handling this optimization problem using anaugmented Lagrangian method. We show that the result-ing algorithms are instances of the alternating directionmethod of multipliers and that the conditions guarantee-ing its convergence are satisfied. Experiments show thatour approach yields state-of-the-art performance.

Mario A. T. FigueiredoInstituto de Telecomunicaoes, Instituto Superior TecnicoLisboa,Portugalmario.figueiredo@lx.it.pt

Jose M. Bioucas-DiasInstituto de TelecomunicacoesInstituto Superior Tecnicobioucas@lx.it.pt

MS17

Multiplicative Noise Removal Using L1 Fidelity onFrame Coefficients

Classical multiplicative noise removal approaches use ei-ther the raw data or its log transform and apply filtering,

Bayesian, variational, or shrinkage methods. We proposea specialized hybrid method combining the advantages ofthese approaches. The restored log-image minimizes a cri-terion combining L1 data-fidelity on the coefficients of ahard-thresholded curvelet transform of the log-data andTV regularization on the log-image. We derive a conver-gent fast scheme based on Douglas-Rachford splitting. Thenumerical results are promising.

Mila NikolovaCentre de Mathematiques et de Leurs Applications(CMLA)ENS de Cachan, CNRSnikolova@cmla.ens-cachan.fr

Sylvain DurandUniversite Rene DescartesParis, Francexxx

Jalal FadiliCNRS-ENSI-CAEN-Universite de CaenCaen, Francexxx

MS17

Frame-based Proximal Algorithms for PoissonData Recovery

We consider convex optimization techniques for data re-covery aiming at minimizing a criterion mixing a spatialdomain regularization (e.g. isotropic or anisotropic totalvariation using various gradient filters), and a transformdomain regularization (e.g. a term promoting sparsity).An accelerated version of the Parallel ProXimal Algorithm(PPXA) is proposed that avoids to invert a large-size lin-ear operator as required by some alternative numerical so-lutions, e.g. the split Bregman method.

Caroline ChauxUniversite Paris-Estcaroline.chaux@univ-mlv.fr

Jean-Christophe Pesquet, Nelly PustelnikUniversite Paris-EstMarne la Vallee, Francexxx, xxx

MS17

A Comparative Review of SAR Images Speckle De-noising Methods Based on Functional Minimiza-tion

Synthetic aperture radar (SAR) as a coherent imagingmodality leads to multiplicative speckle noise. We fo-cus here on discrete MRF energy mimimization-based ap-proaches to filter speckle and on their continuous, varia-tional counterpart. Investigations proposed so far involvein particular: logarithm of the image, variational and aug-mented Lagrangian methods, generalized Lp + Lq modeland graph cuts (joint interferometric phase and amplitudeimage filtering). Those are compared on selected imageswith a common evaluation protocol. This work is funded byFrench Defence Agency contract DGA REI 2008.34.00.42

Jean-Francois AujolCMLA, ENS Cachan, CNRS, UniverSudaujol@cmla.ens-cachan.fr

62 IS10 Abstracts

Emmanuel BratsolisUniversity of Athens, Department of Physics,Panepistimiopolis, GR-15784, Athens, Greeceebrats@phys.uoa.gr

Jerome DarbonCMLA CNRS UMR 8536 Ecole Normale Superieure deCachan,61 avenue du president Wilson 94235 Cachan, Francejerome@berbiqui.org

Loic DenisEcole Superieure de Chimie Physique Electronique deLyon andLaboratoire Hubert Curien, CNRS UMR 5516,St-Etienne, Franceloic.denis@cpe.fr

Jean-Marie Nicolas, Xavier RondeauTELECOM ParisTech, Paris (France)jean-marie.nicolas@telecom-paristech.fr,xavier.rondeau@telecom-paristech.fr

Marc SigelleTELECOM ParisTech,Paris (France)marc.sigelle@telecom-paristech.fr

Florence TupinTELECOM ParisTech, Paris (France)florence.tupin@telecom-paristech.fr

MS17

Gamma and Poissonian Noise Removal

We consider a variational restoration model consisting ofthe I-divergence as data fitting term and the total variationsemi-norm or nonlocal means as regularizer for removingmultiplicative Gamma noise. Although the I-divergence isthe typical data fitting term when dealing with Poissonnoise we substantiate why it is also appropriate for clean-ing Gamma noise. We propose to compute the minimizerof our restoration functional by applying Douglas-Rachfordsplitting techniques, resp. alternating direction methods ofmultipliers, combined with an efficient algorithm to solvethe involved nonlinear systems of equations. We prove theQ-linear convergence of the latter algorithm. Finally, wedemonstrate the performance of our whole scheme by nu-merical examples. (The talk is considered as a possible’fill-in-talk’.)

Tanja TeuberUniversity of Mannheim, Germanytteuber@kiwi.math.uni-mannheim.de

Simon SetzerUniversity of Mannheimssetzer@kiwi.math.uni-mannheim.de

Gabriele SteidlInstitute of Mathematics und Computer ScienceUniversitaet Mannheim, Germanysteidl@math.uni-mannheim.de

MS18

High-resolution Image Reconstruction for Parallel

MR Imaging

Parallel magnetic resonance imaging (pMRI) is a techniquewhich uses multiple receiver coils to speed up data acqui-sition time. Traditionally, down-sampling is applied in theky-direction in frequency domain. The missing informa-tion is recovered from those parallel receiver coils, and anunliasing inversion is needed for reconstruction. Here, wepropose another parallel imaging technique. We scan onlya small region in the frequency domain while maintain-ing the same size of field-of-view. We acquire data froma sequence of receiver coils. Each gives a low-resolutionimage. The missing high-resolution image can be recov-ered from these low-resolution images due to the spatialindependence of the sensitivity functions of these receivercoils.

I-Liang ChernDepartment of MathematicsNational Taiwan Universitychern@math.ntu.edu.tw

MS18

An Image Space Approach to Cartesian Based Par-allel MR Imaging with Total Variation Regulariza-tion

The Cartesian parallel magnetic imaging problem is for-mulated variationally using a high order penalty for mod-ulations and a total variation like penalty for the image.Then the optimality system is derived and numerically dis-cretized. The full problem is first considered in terms ofthe subproblems of modulation correction and aliasing cor-rection. The cost functional used is non-convex, but thederivative of the cost has a bilinear residual term, and thefunctional is convex in each single argument. Thus, convexanalysis is used to formulate the optimality condition forthe image in terms of a primal-dual system. Also, a nonlin-ear Gauss-Seidel iteration is used to minimize with respectto one variable after the other using Newton’s method. Fa-vorable computational results are shown for artifical phan-toms as well as for realistic magnetic resonance images.

Michael HintermuellerHumboldt-University of Berlinhint@math.hu-berlin.de

MS18

Human Brain Mapping using Computational Qua-siconformal Geometry

In Human Brain Mapping, neuroscientists commonly aimto identify structural differences between healthy and un-healthy brains, in order to detect systematic patterns of al-terations in brain diseases. Surface-based cortical analysisis an important strategy and has found useful applicationsin disease analysis. The main obstacle is that the humanbrain cortical surface is a very complicated manifold withdifficult geometry. In this talk, I will describe how confor-mal and quasiconformal geometry can be used to analyzebrain surfaces accurately and systematically. I will firstlydescribe how conformal and quasiconformal maps can becomputed. These maps give the best global parameteriza-tions of cortical surfaces which align landmarks and can beused for various applications such as surface registration,feature detection, computation on surfaces, etc. Secondly,different surfaces with landmarks correspondence have dif-ferent conformal structures. This gives ”signatures” fordifferent brain surfaces for shape analysis. In the second

IS10 Abstracts 63

part of my talk, I will describe how conformal structure ofthe brain surface can be used for shape analysis, using Te-ichmuller theory as a tool. Specifically, I will describe howdifferent conformal modules can be computed and used forabnormality detection in brain surfaces.

Ronald LM LuiDepartment of MathematicsHarvard Universitymalmlui@math.harvard.edu

MS18

Auto-Probing System for Breast Cancer Detectionin Magnetic Resonance Imaging (MRI)

This project aims to develop a breast cancer detection sys-tem with the invention of auto-probing methodology tolocalize and visualize the region of cancerous lesion. Thissystem can reduce the analysis time and enables more thor-ough examination for breast screening. The lesion will becoloured and exposed out on the MR images for betteridentification and verification of the lesions characteristics.The region of interest selection enables the system to gener-ate a graph which contains clearer details about the lesion.Furthermore, higher sensitivity and specificity is expectedto be achieved with this system in comparison to the cur-rent practice where random probing is applied.

Kok Swee SimCentre of Multimedia Security and Signal ProcessingMultimedia University, Malaysiakssim@mmu.edu.my

MS19

Comparing Shape Properties by MultidimensionalPersistent Topology

In this talk we shall briefly illustrate the use of multidi-mensional persistence for shape comparison. Moreover,we shall present some recent theoretical results that wehave obtained about multidimensional persistent topology,proving the stability of multidimensional persistent homol-ogy and showing how its discontinuities can be localized.

Patrizio FrosiniUniversity of BolognaDipartimento di Matematicafrosini@dm.unibo.it

MS19

Metric Geometry in Shape Analysis

The problem of object matching under invariances can bestudied using certain tools from Metric Geometry. Themain idea is to regard objects as metric spaces (or measuremetric spaces). The type of invariance one wishes to havein the matching is encoded in the choice of the metricswith which we endow the objects. The standard example ismatching objects in Euclidean space under rigid isometries:in this situation one would endow the objects with theEuclidean metric. More general scenarios are possible inwhich the desired invariance cannot be reflected by thepreservation of an ambient space metric. Several ideas dueto M. Gromov are useful for approaching this problem.In this talk we discuss different adaptations of these, andin particular we construct an Lp version of the Gromov-

Hausdorff distance using mass transportation ideas.

Facundo MemoliStanford University, Mathematics Departmentmemoli@math.stanford.edu

MS19

Spectral Approaches to Shape Matching, Segmen-tation and Statistical Shape Analysis

Complex geometric objects have gained much importancein many different application fields such as medicine, com-puter aided design or engineering. Modern sensor technolo-gies produce large amounts of 3D (or higher dimensional)data, that need to be analyzed and processed automati-cally. Methods to compare, recognize and process shape(2D surfaces or 3D solid objects) are essential ingredientsto achieve this goal. This talk will give an overview on dif-ferent applications of spectral methods in shape analysis. Iwill demonstrate how the eigenvalues and eigenfunctions ofthe Laplace-Beltrami operator yield powerful tools to de-scribe and analyze shape. Due to their isometry invariancethey are optimally suited to deal with non-rigid shapes of-ten found in nature, such as a body in different postures.The normed beginning sequence of the spectrum can beused as a global signature for shape matching and databaseretrieval, while the eigenfunctions and their topologicalanalysis, employing the Morse-Smale complex, persistencediagram or the Reeb graph, can be applied for shape regis-tration, segmentation and local shape analysis. Examplesof applications such as database retrieval of near isometricshapes, statistical shape analysis of subcortical structuresand hierarchical segmentation of articulated shapes will bepresented.

Martin ReuterMIT-CSAILreuter@mit.edu

MS19

Multiscale Signature Based on Heat Diffusion

We propose a novel point signature based on the proper-ties of the heat diffusion process on a shape. Our signature,called the Heat Kernel signature (or HKS), is obtained byrestricting the well-known heat kernel to the temporal do-main. Remarkably we show that under certain mild as-sumptions, HKS captures all of the information containedin the heat kernel, and characterizes the shape up to isom-etry. This means that the restriction to the temporal do-main, on the one hand, makes HKS much more concise andeasily commensurable, while on the other hand, it preservesall of the information about the intrinsic geometry of theshape. In addition, HKS inherits many useful propertiesfrom the heat kernel, which means, in particular, that it isstable under perturbations of the shape. Our signature alsoprovides a natural and efficiently computable multi-scaleway to capture information about neighborhoods of a givenpoint, which can be extremely useful in many applications.To demonstrate the practical relevance of our signature, wepresent several methods for non-rigid multi-scale matchingbased on the HKS and use it to detect repeated structurewithin the same shape and across a collection of shapes.

Jian SunStanford-CSsunjian@stanford.edu

Maks Ovsjanikov, Leonidas Guibas

64 IS10 Abstracts

Stanford Universitymaks@stanford.edu, guibas@cs.stanford.edu

MS20

Image Compression with Anisotropic Geodesic Tri-angulations

We propose to compress images using anisotropic Delau-nay triangulations generated from a Riemannian farthestpoint seeding strategy. This seeding forces triangles to fol-low sharp edges and directional features. The compressionis achieved by approximating images by linear splines overthe triangulations, and by coding both the spline coeffi-cients and the deviation of the anisotropic triangulationsfrom the Euclidean Delaunay triangulation. The resultingencoder competes well, on geometric images, with wavelet-based encoders such as JPEG-2000.

Sebastien BougleuxUniversity of CaenGREYC CNRSsebastien.bougleux@unicaen.fr

Gabriel PeyreCEREMADE, Universite Paris Dauphinepeyre@ceremade.dauphine.fr

Laurent D. COHENCEREMADE, Universite Paris Dauphine and CNRScohen@ceremade.dauphine.fr

MS20

A Tubular Model for Orientation Dependent VesselSegmentation Using Anisotropic Fast Marching

We present a new interactive method for tubular structureextraction, like vessels in 2D and 3D images. The basictools are minimal paths solved using the fast marching al-gorithm. Our method is based on a variant of the minimalpath method that models the vessel as a centerline andsurface. The crucial step of our method is the definition ofthe local metrics to minimize. We have chosen to exploitthe tubular structure of the vessels one wants to extractto built an anisotropic metric. The designed metric is welloriented along the direction of the vessel, admits highervelocity on the centerline, and provides a good estimate ofthe vessel radius. Based on the optimally oriented flux thismeasure is required to be robust against the disturbanceintroduced by noise or adjacent structures with intensitysimilar to the target vessel.

Laurent D. CohenCNRS, UMR 7534Universite Paris-Dauphine, CEREMADEcohen@ceremade.dauphine.fr

Fethallah BenmansourCEREMADE, Universite Paris Dauphinebenmansour@ceremade.dauphine.fr

MS20

Brain Connectivity Mapping Using RiemannianGeometry, Control Theory and PDEs

We introduce an original approach for the mapping of thecerebral white matter connectivity from diffusion tensorimaging (DTI). Our method relies on a global modeling ofthe acquired MRI volume as a Riemannian manifold whose

metric directly derives from the diffusion tensor. Thesetensors will be used to measure physical three-dimensionaldistances between different locations of a brain diffusiontensor image. The key concept is the notion of geodesic dis-tance that will allow us to find optimal paths in the whitematter. Such optimal paths are reasonable approximationsof neural fiber bundles. The geodesic distance function canbe seen as the solution of two theoretically equivalent but,in practice, significantly different problems in the partialdifferential equation framework: an initial value problemwhich is intrinsically dynamic, and a boundary value prob-lem which is, on the contrary, intrinsically stationary. Thetwo approaches have very different properties which makethem more or less adequate for our problem and more orless computationally efficient. The dynamic formulationis quite easy to implement but has several practical draw-backs. On the contrary, the stationary formulation is muchmore tedious to implement; we will show, however, that ithas many virtues which make it more suitable for our con-nectivity mapping problem.

Christophe LengletDepartment of Electrical and Computer EngineeringUniversity of Minnesotaclenglet@umn.edu

Emmanuel PradosINRIA Rhemmanuel.prados@inrialpes.fr

Jean-Philippe PonsCentre Scientifique et Technique du Batimentjean-philippe.pons@cstb.fr

Rachid DericheOdyssee Lab, INRIA Sophia AntipolisRachid.Deriche@sophia.inria.fr

Olivier FaugerasINRIAOlivier.Faugeras@sophia.inria.fr

MS20

Restrictions of the Fast-marching-method for theAnisotropic Eikonal Equation

In many applications one wants to solve the anisotropiceikonal equation on a given cartesian grid. Using the8-point (or the 4-point) neighborhood discretisation onelooses the causality property of the update formulae if theanisotropy has certain properties. We discuss this situationand state cirteria to decide wether the discretization is suit-able for the given problem or not. Furthermore we presenta method which can deal in general with anisotropy. Thismethod uses virtual updates, analogue to the virtual up-dates on unstructured triangulations [James A. Sethian.Level set methods and fast marching methods. Evolv-ing interfaces in computational geometry, fluid mechanics,computer vision, and materials science. Cambridge Mono-graphs on Applied and Computational Mathematics, 1999]and it uses the same idea to handle anisotropy as it isdone in [Folkmar Bornemann and Christian Rasch. Finite-element discretization of static Hamilton-Jacobi equationsbased on a local variational principle. Comput. VisualSci., 9:57; 69, 2006].

Thomas SatzgerTechnische Universitat Munchensatzger@ma.tum.de

IS10 Abstracts 65

MS20

Anisotropic Fast Marching in PathophysiologicalModeling

Bridging the gap between clinical applications and patho-physiological models is one of the new challenges of med-ical image analysis. In this work, we propose an efficientand accurate algorithm to solve anisotropic Eikonal equa-tions, in order to link mathematical models using reaction-diffusion equations to sparse clinical observations, such asmedical images. We use the proposed algorithm in two dif-ferent modelling applications: tumour growth and cardiacelectrophysiology.

Ender konukogluINRIA Sophie Antipolisender.konukoglu@sophia.inria.fr

Maxime Sermesant, Phani Chinchapatnam, NicholasAyacheINRIAmaxime.sermesant@sophia.inria.fr,phani.chinchapatnam@sophia.inria.fr,nicholas.ayache@sophia.inria.fr

MS21

FaIMS: A Fast Algorithm for the Inverse MediumProblem in Acoustic Scattering

We consider the inverse medium problem for the time-harmonic wave equation with broadband and multi-pointillumination in the low frequency regime. Such a prob-lem finds many applications in geosciences (e.g. groundpenetrating radar), non-destructive evaluation (acoustics),and medicine (optical tomography). We use an integral-equation (Lippmann-Schwinger) formulation, which wediscretize using a quadrature method. We consider onlysmall perturbations (Born approximation). To solvethis inverse problem, we use a least-squares formulation.We present a new fast algorithm for the efficient so-lution of this particular least-squares problem. If Nf

is the number of excitation frequencies, Ns the numberof the different source locations of the point illumina-tions, Nd the number of detectors, and N the discretiza-tion size for the scatterer, a dense singular value de-composition for the overall input-output map will have[min(NsNfNd, N)]2×max(NsNfNd, N) cost. We have de-veloped a fast SVD-based preconditioner that brings thecost down to O(NsNfNdN) thus, providing orders of mag-nitude improvements over a black-box dense SVD or anunpreconditioned linear iterative solver.

George Biros, Stephanie ChaillatGeorgia Institute of Technologybiros@gatech.edu, stephanie.chaillat@cc.gatech.edu

MS21

Regularization in a Multichannel Framework forProblems Arising in Image Processing Applications

Ill-posed inverse problems arise in a variety of significantapplications in image processing, and efficient regulariza-tion methods are needed to compute meaningful solutions.The algorithms for image reconstruction that are discussedhere are based on transforming an image into some fre-quency domain and incorporating regularized inversion andwavelet filtering methods within a multichannel framework.Numerical algorithms for the choice of the regularizationand filtering parameters will be discussed, and examples

from image deblurring will be presented.

Julianne ChungUniversity of Marylandjmchung@cs.umd.edu

Glenn EasleySystems Planning Corporationgeasley@sysplan.com

Dianne P. O’LearyUniversity of Maryland, College ParkDepartment of Computer Scienceoleary@cs.umd.edu

MS21

Obtaining Better Images - Design in Imaging

Obtaining better images can be done by combining soft-ware and hardware. In this talk we present a general frame-work that allows for designing better instrumentation andreconstruction algorithms. We show that such frameworkleads to a large scale stochastic optimization problem. Wethen suggest a few approaches for the solution of the prob-lem. We show the effectiveness of our method using a fewimaging methods such as limited angle tomography andsuper resolution

Eldad HaberDepartment of MathematicsThe University of British Columbiahaber@math.ubc.ca

MS21

Deblurring for Related Images Using Hybrid Reg-ularization for Multiple Right Hand Systems

Image deblurring is ill-posed, even for blur described by aspatially invariant linear operator. In this talk we focuson deblurring of large scale problems using Tikhonov reg-ularization applied at the local level as part of a domaindecomposition algorithm. The global iterative approachrequires that solutions are obtained of the subproblem sys-tem for multiple right hand sides, where each right handside depends on the current global iterative solution. Thealgorithm is made more efficient by using updating of theinitial local Krylov subspaces per problem with minimalrestarts. Our numerical results illustrate the feasibility ofthe approach.

Rosemary A. RenautArizona State UniversitySchool of Mathematical and Statistical Sciencesrenaut@asu.edu

Youzuo LinArizona State Universityyouzuo.lin@asu.edu

MS22

Variational Photometric Stereo

It is well-known that photometric stereo data provides lo-cal information surface normals and the depth data mustsubsequently be reconsidered via an integration process.In this talk, we shall discuss ways to combine the use oflocal data and surface integration into a single depth from

66 IS10 Abstracts

photometric stereo variational functional.

Alfred M. BrucksteinComputer Science DepartmentTechnion IIT, Haifa, Israelfreddy@cs.technion.ac.il

MS22

Multigrid Narrow Band Surface Reconstruction viaLevel Set Functions

In this talk I will discuss a new method for implicit surfacereconstruction from unorganized point clouds. Our algo-rithm employs a multigrid solver on a narrow band, whichgreatly improves the computational efficiency of surface re-construction process. The new model can reconstruct sur-faces from noisy unorganized point clouds that also havemissing information. Comparing to traditional methods,our method is significantly faster and the reconstructedsurfaces have detailed information.

Bin DongUCSDb1dong@math.ucsd.edu

Jian YeMathematics, UCLAye@math.ucla.edu

Igor YanovskyJet Propulsion Laboratory, California Institute ofTechnologigor.yanovsky@jpl.nasa.gov

Rima GandlinDepartment of MathematicsCarnegie Mellon Universityrima121212@gmail.com

Achi BrandtUCLAabrandt@math.ucla.edu

Stanley J. OsherUniversity of CaliforniaDepartment of Mathematicssjo@math.ucla.edu

MS22

Surface Reconstruction and Shading from SparseGradient Fields Based on Vector Inpainting

We propose vector inpainting methods for reconstructinga surface from given strokes which usually make a shape ofobject to look like 3D surface. After initial vectors are as-signed on the stokes, the vectors are distributed via a func-tional minimization with the incompressibility constraintwhich is the alternative condition of forcing the integrabil-ity condition in typical surface reconstruction. We applythe proposed method to generate anime-like shading.

Jooyoung HahnDivision of Mathematical SciencesNayang Technological Universityjyhahn@ntu.edu.sg

Xue-cheng TaiDept. of Mathematics, University of Bergen, Norway and

Div. of Math. Sciences, Nanyang Tech. Universitytai@mi.uib.no

Eiji Sugisaki, Jie Qiu, Lei Jia, Hock Soon SeahSchool of Computer EngineeringNanyang Technological Universityseiji@ntu.edu.sg, jqiu@ntu.edu.sg, jialei@ntu.edu.sg,ashsseah@ntu.edu.sg

MS22

Augmented Largrangian Method, Dual Methodsand Split Bregman Iteration for ROF, Vectorial TVand High Order Models

In this talk, the augmented Lagrangian method is appliedto overcome the non-differentiability and to make fast nu-merical schemes of the ROF model. We observe close con-nections between the method proposed here and some ofthe existing methods, such as the dual method of CGMand Chambolle, split Bregman iteration, and splitting andpenalty based method. Moreover, our method are easilyextended to vectorial TV and high order models.

Chunlin WuSchool of Physical and Mathematical SciencesNanyang Technological Universityclwu@ntu.edu.sg

Xue-cheng TaiDept. of Mathematics, University of Bergen, Norway andDiv. of Math. Sciences, Nanyang Tech. Universitytai@mi.uib.no

MS23

Microlocal Analysis of the Geometric SeparationProblem

Images are often composed of two or more geometri-cally distinct constituents; in neurobiological imaging, forinstance, point-structures (spines) and curve-structures(dendrites) are mixed. We will present a theoretical anal-ysis showing that accurate geometric separation of pointand curve singularities can be achieved by minimizingthe �1-norm or thresholding the coefficients of a wavelet-curvelet/shearlet-dictionary. Driving our analysis is theclustered sparsity of the ideal coefficients in microlocalphase space.

Gitta KutyniokUniversity of Osnabrueckkutyniok@uni-osnabrueck.de

David L. DonohoStanford UniversityDepartment of Statisticsdonoho@stanford.edu

MS23

Characterization of Singularities and Edge Detec-tion using the Continuous Shearlet Transform

Directional multiscale systems such as the Shearlet Trans-form were recently introduced to overcome the limitationsof the traditional wavelet transform in dealing with mul-tidimensional data. In fact, while the continuous wavelettransform is able to identify the location of singularities offunctions and distributions through its asymptotic behav-ior at fine scale, it lacks the ability to capture the geometry

IS10 Abstracts 67

of the singularity set. In this talk, we show that the Shear-let Transform has the ability to precisely characterize boththe location and orientation of the set of singularities of 2Dand 3D functions. This is relevant in imaging applicationssuch as edge detection and feature extraction.

Demetrio LabateUniversity of Houstondlabate@math.uh.edu

MS23

Microlocal Analysis and Travel Time Tomography

We consider the problem of determining the anisotropicindex of refraction of a medium by measuring the traveltimes of waves going through the medium. We considerboth the case of transmission tomography and reflectiontomography.

Gunther UhlmannUniversity of Washingtongunther@math.washington.edu

MS23

Doppler Synthetic Aperture Hitchhiker Imaging

In this talk, we consider passive airborne receivers that usebackscattered signals from sources of opportunity trans-mitting fixed-frequency waveforms. Due to its combinedpassive synthetic aperture and the fixedfrequency natureof the transmitted waveforms, we refer to the system underconsideration as Doppler Synthetic Aperture Hitchhiker(DSAH). We present a novel image formation method forDSAH. Our method first correlates the windowed signal ob-tained from one receiver with the windowed, filtered, scaledand translated version of the received signal from anotherreceiver. This processing removes the transmitter relatedvariables from the phase of the Fourier integral operatorthat maps the radiance of the scene to the correlated sig-nal. We, next, use the microlocal analysis to reconstructthe scene radiance by the weighted-backprojection of thecorrelated signal. The image reconstruction method is ap-plicable with both cooperative and non-cooperative sourcesof opportunity using one or more airborne receivers. It hasthe desirable property of preserving the visible edges ofthe scene radiance. Additionally, it is an analytic recon-struction technique which can be made computationally ef-ficient. We present numerical simulations to demonstratethe performance of the image reconstruction method andto verify the theoretical results.

Birsen YaziciDepartment of Electrical, Computer and SystemsEngineeringRensselaer Polytechnic Instituteyazici@ecse.rpi.edu

MS24

Non-local Filtering of Images Using Data-drivenTransforms

We consider the so-called grouping and collaborative filter-ing approach: similar patches in an image or video are col-lected and jointly transformed using a higher-dimensionaltransform, sparsity is then enforced by shrinkage of thehigher-dimensional spectrum. This approach has provedto be very successful, especially as the core element of de-noising, deblurring, and other inverse filtering algorithms.We discuss various aspects related to the adaptivity of the

transforms used in collaborative filtering, with particularemphasis on the geometrical adaptation and on the learn-ing of basis elements from noisy data.

Alessandro FoiDepartment of Signal ProcessingTampere University of Technology, Finlandalessandro.foi@tut.fi

Vladimir Katkovnik, Karen EgiazarianTampere University of Technologyvladimir.katkovnik@tut.fi, karen.egiazarian@tut.fi

MS24

Another Role for Sparsity in Pattern Matching: ASimple, First-principle Derivation Based on Com-putational Complexity

We consider pattern matching problems where a patternlibrary, a set consisting of a large number of vectors, isto be queried for the presence of user-provided patternsin a Neyman-Pearson setting. Without any constraintson computational complexity, it is clear that one can an-swer such queries with arbitrarily high accuracy. Establish-ing computational complexity as the fundamental resourcethat needs to be traded with matching accuracy, our ap-proach formulates the search problem as the maximizationof accuracy for a given constraint in computational com-plexity. In effect, our work represents the pattern library interms of its computational-complexity-dependent approx-imations, where coarser approximations are computation-ally easier to search but lead to less accurate results. Oursolutions naturally lead to sparse approximations, estab-lishing a duality between sparse decompositions and pat-tern matching problems: (a) Patterns that are easy to findmust be sparse in some domain, (b) with low computa-tional complexity, one can only hope to reliably find sparseapproximations of patterns.

Onur GuleryuzDoCoMo Communications Laboratories USAguleryuz@docomolabs-usa.com

MS24

Local and Non-local Similarity for Visual Recogni-tion From a Single Example

We present a novel framework for detection/recognition ofvisual (2-D and 3-D) objects without training. The pro-posed framework operates using one example (query) of anobject of interest to find similar matches; does not requireprior knowledge (learning) about objects being sought; anddoes not require any pre-processing step or segmentationof a target image/video. Our method is based on the com-putation of local regression kernels as descriptors from aquery, which measure the likeness of a pixel, voxel, orpatch, to its surroundings. State of the art performanceis demonstrated on challenging datasets in several visualprocessing tasks including generic detection and recogni-tion of visual objects in 2-D and actions in 3-D, in diversecontexts and under varying imaging conditions. In addi-tion, using the patch-based framework, we are able to ro-bustly and accurately capture visually salient objects andtheir boundaries, closely mimicking human fixation data inboth static and dynamic scenes.

Hae Jong Seo, Peyman MilanfarEE DepartmentUniversity of California, Santa Cruz

68 IS10 Abstracts

rokaf@soe.ucsc.edu, milanfar@ee.ucsc.edu

MS24

Universal Sparse Modeling

The goal of this talk is to make formal connections betweensparse modeling and information theory, and in particular,universal coding and MDL. We will show how this leadsto novel sparsity-inducing priors which have a number ofadvantages over more classical l0 and l1 ones. Joint workwith I. Ramirez and F. Lecumberry.

Guillermo SapiroUniversity of MinnesotaDept Electrical & Computer Engineeringguille@umn.edu

MS25

Analytic Sensing: A New Approach to SourceImaging and Its Application to EEG

Electroencephalography (EEG) provides us with a non-invasive way to access information about the brain’s cor-tical activity. Mapping back the electrical potential mea-sured on the scalp to the underlying source configurationis known as ”source imaging”. To render the problem well-posed, additional constraints on the solution are needed.Specifically, we use a parametric source model (sum ofdipoles) and we propose a new framework termed ”ana-lytic sensing,” that lead to a non-iterative technique formulti-dipole fitting. The key contribution is to apply ana-lytic test functions that ”sense” the influence of the sourcedistribution around virtual sensors. The choice of thesesensors allows us to estimate the dipoles’ positions by find-ing an annihilation filter similar to ”finite rate of innova-tion” techniques. We show how to apply analytic sensing to3D and to EEG in particular. Preliminary results demon-strate the technique’s potential to retrieve multiple dipolesat once, a problem that is difficult to solve by (numerical)least-squares fitting due to the many local minima. Jointwork with: D. Kandaswamy, D. Van De Ville

Thierry BluDepartment of Electronic EngineeringThe Chinese University of Hong Kongtblu@ee.cuhk.edu.hk

Djano Kandaswamy, Dimitri Van De VilleBiomedical Imaging GroupEcole Polytechnique Federale de Lausannedjano.kandaswamy@epfl.ch, dimitri.vandeville@epfl.ch

MS25

High Order Vector-valued Models for ImageRestoration

Variational techniques for gray-scale image restorationhave been deeply investigated for many years, however,little research has been done for the vector-valued caseand the very few existent works are total-variation-basedmodels [P. Blomgren and T.F. Chan. Color TV: to-tal variation methods for restoration of vector-valued im-ages. IEEE Transactions on Image Processing, 7(3):304-309,1998; X. Bresson and T.F. Chan. Fast dual mini-mization of the vectorial total variation norm and appli-cations to color image processing. Inverse Problems andImaging, 2(4):455-484, 2008; G. Sapiro and D.L. Ringach.Anisotropic diffusion of multivalued images with applica-

tions to color filtering. IEEE Transactions on Image Pro-cessing, 5(11):1582-1586, 1996; Wei Zhu and T. F. Chan.Image denoising using mean curvature. Preprint availablefrom http://www.math.nyu.edu/∼wzhu/]. For instance,it is known that TV models (and variants including graphcuts based models) suffer from staircasing effect in imagedenoising and fail to deliver a visually satisfactory recon-struction in many situations in image inpainting where im-ages cannot be assumed to be piecewise constants. Further,the same arguments carry over to the vector-valued mod-els. High order models, on the contrary, do not presentstaircasing in image denoising, and allow large distancereconnection and smooth recovery of missing parts in im-age inpainting. In this work we first propose and analyzetwo high order and curvature-based denoising models forvector-valued images which allow stronger coupling amongdifferent channels than a channel-by-channel approach fora given noisy vector-valued image u0

minu1,...,um

⎧⎨⎩

∫Ω

√√√√ m∑�=1

Φ�(κ�) dx +λ

2

∫Ω

|u − u0|2 dx

⎫⎬⎭

minu1,...,um

⎧⎨⎩

√√√√∫Ω

m∑�=1

Φ�(κ�) dx +λ

2

∫Ω

|u − u0|2 dx

⎫⎬⎭

where u = Ω ⊂ Rn → Rm i.e., u = (u1, . . . , um) with u� =u�(x1, . . . , xn) ∀ � = 1, . . . , m, dx = (dx1, . . . , dxm), κ�

the curvature of �th image channel and Φ a given function.Then a fast multigrid algorithm for the numerical solutionis developed and tested. Advantages over TV based andother coupling models are illustrated. Finally extensionof these techniques to color image inpainting is consideredand some preliminary results are reported.

Carlos BritoUniversity of Liverpool, UKcbrito@liv.ac.uk

Ke ChenUniversity of Liverpoolk.chen@liverpool.ac.uk

MS25

Iterative Methods for Image Reconstruction andApplications to Bioluminescence Tomography

Iterative methods for image reconstruction have becomevery popular today for imaging research and applications.The Landweber method and EM algorithm are widely usedmethods for image reconstruction. I will first introducethe Landweber method and the EM algorithm. Then Iwill report our progress about bioluminescence tomography(BLT). BLT is an emerging molecular imaging techniquein the form of an ill-posed inverse source problem subjectto Cauchy data of the diffusion equation.

Ming JiangSchool of Mathematical SciencesPeking Universityming-jiang@pku.edu.cn

MS25

Source Reconstruction for Spectrally-resolved Bi-oluminescence Tomography with Sparse A prioriInformation

We develop a new tomographic algorithm for spectrally-

IS10 Abstracts 69

resolved bioluminescence tomography. This method usesthe nature of the source sparsity to improve the reconstruc-tion quality with a regularization implementation. Basedon verification of the inverse crime, the proposed algorithmis validated with Monte Carlo-based synthetic data andthe popular Tikhonov regulariz ion method. Testing withdifferent noise levels and single/multiple source settings atdifferent depths demonstrates the improved performance ofthis algorithm. Experimental reconstruction with a mouse-shaped phantom further shows the potential of the pro-posed algorithm.

Xiaoqun ZhangUniversity of California Los Angeles.xqzhang@math.ucla.edu

MS26

Regularizing with Anisotropic Total Variation

Total variation regularization has been used for image de-noising for about twenty years now. These regularizationshave other uses as well; in particular, they can be usedto detect differences in scales in data. I have been study-ing the geometric and regularity properties of minimizersfor the associated variational problems with the goal ofbetter understanding them. In this talk I will describesome new results in this area. Some of these results de-scribe minimizers where total variation is defined using ananisotropic norm for the gradient; the motivation for thiswork, which is joint with Kevin Vixie, is that some compu-tational schemes for computing minimizers naturally use apolygonal approximation to the standard Euclidean metricto define total variation.

William AllardDuke UniversityDepartment of Mathematicswka@math.duke.edu

Kevin R. VixieWashington State Universityvixie@speakeasy.net

MS26

Calibrable Sets and Scales for TV-L2 and TV-L1Models

In this talk, we address the problem of scale definition,based on the notion of calibrable set. In a first part, weexplain how the TV-L2 model can be used to define thescale of an object. In a second part, we consider the TV-L1 model, and we show how this functional discriminatesbetween structure and texture according to the previousdefinition of scale. This work has been supported by theFrench ”Agence Nationale de la Recherche” (ANR), un-der grants NATIMAGES (ANR-08-EMER-009) ”Adaptiv-ity for natural images and texture representations” andFREEDOM (ANR07-JCJC-0048-01),”Movies, restorationand missing data”.

Jean-Francois AujolCMLA, ENS Cachan, CNRS, UniverSudaujol@cmla.ens-cachan.fr

Vincent DuvalTelecom Paris Techvduval@enst.fr

Yann Gousseau

Telecom Parisgousseau@enst.fr

MS26

Multiscale Image Representation Using a NovelIntegro-differential Equations

We propose a novel integro-differential equation (IDE) fora multiscale image representation. To this end, one inte-grates in inverse scale space a succession of refined ‘slices’of the image, which are balanced by a typical curvatureterm at the finer scale. The original motivation camefrom a variational-based hierarchical decomposition of im-ages. We then use standard techniques from PDE-basedimage processing - filtering, edge preserving and tangen-tial smoothing, to yield a family of modified IDE modelswith applications to image denoising and deblurring prob-lems. The IDE models depend on a user scaling functionwhich is shown to dictate the BV properties of the residualerror. Numerical experiments demonstrate applications ofour new IDE approach.

Eitan TadmorUniversity of MarylandUSAtadmor@cscamm.umd.edu

Prashant AthavaDepartment of MathematicsUniversity of Marylandprashant@math.ucla.edu

MS26

Image Restoration Using One-dimensional Profilesof Sobolev Norms for Noise and Texture

We propose a variational model for image denoising anddeblurring, using total variation and Sobolev norms of neg-ative degree of differentiability. The unknown image is re-covered as the sum of two components, cartoon and tex-ture. We impose prior information on the texture and onthe noise, by learning one-dimensional profiles of Sobolevnorms of textures and noise components. These profilesassign to each negative exponent, the Sobolev norm of thetexture or of the noise. Experimental results for joint de-blurring and denoising are shown.

Yunho KimDepartment of Mathematics, UCIyunhok@uci.edu

John B. GarnettDepartment of Mathematics, UCLAjbg@math.ucla.edu

Luminita A. VeseUniversity of California, Los AngelesDepartment of Mathematicslvese@math.ucla.edu

MS27

New Theory and Algorithms for Nonsmooth, Non-convex Minimization

In recent years, nonsmooth, nonconvex minimization hasbecome essential in image restoration. In this talk, we dis-cuss some new algorithms for solving nonsmooth, noncon-vex optimization. Moreover, we present a lower bound the-

70 IS10 Abstracts

ory for the absolute value of nonzero entries in every localminimizer of an objective function composed of a quadraticdata-fidelity term and a nonconvex, non-Lipschitz regular-ization term. This theory can be used to eliminate zeroentries precisely in any numerical solution. Furthermore,it clearly shows the relationship between the sparsity ofthe solution and the choice of the regularization parame-ters, so that the lower bound theory can be used for se-lecting desired model parameters. We also develop errorbounds for verifying the accuracy of numerical minimiz-ers. To demonstrate applications of our theory, we pro-pose an orthogonal matching pursuit-smoothing conjugategradient (OMP-SCG) hybrid method for solving the non-convex, non-Lipschitz minimization problem. Computa-tional results show the effectiveness of the lower boundsfor identifying nonzero entries in numerical solutions andthe OMP-SCG method for finding a high quality numericalsolution.

Xiaojun ChenDepartment of Applied MathematicsThe Hong Kong Polytechnic Universitymaxjchen@polyu.edu.hk

MS27

Lower Semi-Continuity of Non-Local Functionals

We recall a few of the recent non-local methods usedin imaging analysis such as the non-local mean filterand the derivative-free formulation of the total vari-ation functional. Such non-local methods for filter-ing images have proven to handle especially repetitivestructures as for instance textures much better thanclassical PDE-based approaches. Trying to formulatethese methods as energy minimisation problems, wetypically end up with energy functionals of the formJ () =

∫X

∫X {(§, †,(§),(†))dxdy on some Lebesgue

spaces. We give a criterion for these energy functionalsto possess a minimising point. The crucial part thereby isthe weak sequential lower semi-continuity of the function-als which essentially reduces to the separate convexity ofthe function f in the last two variables.

Peter ElbauRICAMpeter.elbau@oeaw.ac.at

MS27

Sparse Regularization with Non-convex Regular-ization Terms

We consider the stable solution of ill-posed operator equa-tions by means of non-convex Tikhonov regularization,where the regularization term acts separately on the co-efficients of an expansion with respect to a given basis, forinstance a Fourier or wavelet basis. We discuss conditionsthat guarantee that such an approach yields a well-posedregularization method. In addition, we derive a linear con-vergence rate under the assumption of infinitely fast growthat zero, a condition that can only be satisfied with non-convex regularization terms.

Markus GrasmairComputational Science CenterUniversity of Vienna, Austriamarkus.grasmair@univie.ac.at

MS27

Convex Relaxations of Metrics for Imaging withMissing Data

The usual presentation of missing data/compressive sens-ing problems is to consider the function ‖ · ‖0 as the limitof the p-metrics as p ↘ 0. The problem with p < 1 isthat the metric is nonconvex and convergence results fornumerical algorithms based on this are difficult at the veryleast. We present an alternative approach based on regu-larization of the Fenchel conjugates of these metrics. Wepropose solving

minx∈Rn

Iϕ∗ε,L

(x) such that Ax = b (1)

where Iϕ∗ε,L

(x) is an entropy with integrand ϕ∗ε,L and relax-

ation parameters ε and L that corresponds to a symmetricscaled Fermi-Dirac entropy. This is a smooth convex re-laxation of the conventional �p optimization for 0 ≤ p ≤ 1and amenable to rigorous analysis and efficient algorithms.

Russell LukeDept of Mathematics, University of DelawareNewark, Delaware 19716rluke@math.udel.edu

MS28

Joint Manifolds for Data Fusion

The emergence of low-cost sensing architectures for diversemodalities has made it possible to deploy camera networksthat capture a single event from a large number of van-tage points and using multiple modalities. In many sce-narios, these networks acquire large amounts of very high-dimensional data. Even a relatively small network of cam-eras can generate massive amounts of high-dimensional im-age and video data. One way to cope with such a datadeluge is to develop low-dimensional data models. Mani-fold models provide a particularly powerful theoretical andalgorithmic framework for capturing the structure of datagoverned by a low-dimensional set of parameters, as is of-ten the case in a sensor network. However, these mod-els do not typically take into account dependencies amongmultiple sensors. We thus propose a new joint manifoldframework for data ensembles that exploits such depen-dencies. We show that joint manifold structure can leadto improved performance for a variety of signal process-ing algorithms for applications including classification andmanifold learning. Additionally, recent results concerningrandom projections of manifolds enable us to formulate anetwork-scalable dimensionality reduction scheme that ef-ficiently fuses the data from all sensors.

Richard G. BaraniukRice UniversityElectrical and Computer Engineering Departmentrichb@rice.edu

Mark Davenport, Chinmay HedgeRice Universitymd@rice.edu, chinmay@rice.edu

Marco F. DuartePrinceton Universitymduarte@princeton.edu

IS10 Abstracts 71

MS28

Distilled Sensing for Imaging

With the recent emergence of sparsity-exploiting technolo-gies (as in compressive sensing), a renewed emphasis hasbeen placed on techniques that make judicious use of sam-pling resources. In particular, adaptive sampling tech-niques, where the sampling process is allowed to adapt orfocus as a function of measurements previously obtained,are promising approaches for mitigating the effects of ad-ditive noise in sparse recovery problems. In this talk I willdiscuss our recent work on Distilled Sensing (DS), whichquantifies the surprising and dramatic improvements thatare achievable using adaptivity. For example, we show thatadaptivity enables the reliable recovery (detection and esti-mation) of sparse signals in prohibitively-low SNR regimeswhere the best methods based on non-adaptive samplingfail. In the context of imaging, DS can lead to significantimprovements in estimation accuracy.

Rob NowakDepartment of Electrical and Computer EngineeringUniversity of Wisconsin-Madisonnowak@ece.wisc.edu

Jarvis HauptRice Universityjdhaupt@rice.edu

Rui CastroColumbia Universityrmcastro@ee.columbia.edu

MS28

Compressive Sensing and Underwater Acoustics

We will discuss the application of the theory of compressivesensing to two problems encountered in acoustics: sourcelocalization/tracking and communication over an uncertainchannel. For the first problem, we show how a randomizedgroup testing can significantly reduce the number of acous-tic simulations needed to locate and then track a source.For the second problem, we treat the scenario of communi-cating over an unknown channel as a blind deconvolutionproblem, and show that if the (unknown) channel is sparseand a random encoding scheme with a small amount ofredundancy is used by the source, then the receiver candiscover both the message and the channel response bysolving a well-posed optimization program.

Justin RombergSchool of ECEGeorgia Techjrom@ece.gatech.edu

William Mantzel, Salman Asif, Karim SabraGeorgia Institute of Technologywillem@gatech.edu, sasif@gatech.edu,karim.sabra@me.gatech.edu

MS28

Finding Structure with Randomness: StochasticAlgorithms for Constructing Low-rank Matrix De-compositions

Computer scientists have long known that randomness canbe used to improve the performance of algorithms. A fa-miliar application is the process of dimension reduction,in which a random map transports data from a high-

dimensional space to a lower-dimensional space while ap-proximately preserving some geometric properties. By op-erating with the compact representation of the data, itis theoretically possible to produce approximate solutionsto certain large problems very efficiently. Recently, it hasbeen observed that dimension reduction has powerful appli-cations in numerical linear algebra and numerical analysis.This talk provides a high-level introduction to randomizedmethods for computing standard matrix approximations,and it summarizes a new analysis that offers (nearly) op-timal bounds on the performance of these methods. Inpractice, the techniques are so effective that they competewith—or even outperform—classical algorithms. Since ma-trix approximations play a ubiquitous role in areas rang-ing from information processing to scientific computing,it seems certain that randomized algorithms will eventu-ally supplant the standard methods in some applicationdomains.

Joel TroppApplied and Computational MathematicsCaltechjtropp@acm.caltech.edu

MS29

Exploiting the Structure of Regularizers for RapidSolution of Euler-Lagrange Equations in Varia-tional Image Registration

Variational image registration techniques combine imagesimilarity measures with regularization terms in order toguarantee that the resulting functional minimization prob-lem is well-posed. In practice, typical regularization termsare quadratic differential forms that can be either spatiallyhomogeneous or adaptive. In this talk, we describe twodifferent rapid computing paradigms for estimating the so-lution to the Euler-Lagrange equations resulting from var-ious families of regularizers; one paradigm uses Fourier se-ries solutions of the discretized Euler-Lagrange equations;the second employs convolution with a discretized Gaussiankernel to mimic the Green’s function solution to coupledPDE systems related to the Euler-Lagrange equations.

Nathan D. CahillSchool of Mathematical SciencesRochester Institute of Technologyndcsma@rit.edu

MS29

A PDE Approach to Coupled Super-Resolutionwith Non-Parametric Motion

The problem of recovering a high-resolution image from aset of distorted low-resolution images is known as super-resolution. Accurate motion estimation among the low-resolution measurements is a fundamental challenge of thesuper-resolution problem. Some recent advances in thisarea have been focused on coupling the super-resolutionreconstruction and the motion estimation. However, theexisting approach is limited to parametric motion mod-els. We will address the coupled super-resolution problemwith a non-parametric motion model in a variational for-mulation. A PDE-approach will be proposed to yield anumerical scheme.

Mehran EbrahimiDept. of Medical BiophysicsUniversity of Torontomehran@sri.utoronto.ca

72 IS10 Abstracts

MS29

Numerical Optimization for Constrained ImageRegistration

Image registration is a technique to establish meaningfulcorrespondences between points in different scenes. It isan inevitable tool for various applications in medicine, geo-science, and other disciplines. However, obtaining reason-able deformations is a complex task. For example, manyapplications require that the transformation is locally in-vertible, or even harder, keeps volumes changes within areasonable bandwidth. In this work, solutions to the regis-tration problem are obtained by directly imposing a volumeconstraint on each voxel in a discretized domain. The focusis on the development of an efficient and robust numericalalgorithm and in particular, the study of an Augmented La-grangian method with a multigrid as preconditioned. Wedemonstrate that this combination yields an almost opti-mal solver (i.e. linear time) for the problem.

Raya HoreshEmory UniversityAtlanta, GArshindm@emory.edu

Eldad HaberDepartment of MathematicsThe University of British Columbiahaber@math.ubc.ca

MS29

Accelerating Non-Rigid Image Registration onGpus

Non-rigid image registration tries to find a suitable defor-mation field between two images that map one image intothe other. This is widely used in medical imaging applica-tions. Here, it is important to have fast image registrationalgorithms, e.g. in order to reduce the waiting time for thepatient or to be able to register images during a surgery.We show how compute intensive parts of the image regis-tration algorithm can be parallelized and ported to GPUsand how the GPU code can be coupled to the FAIR (Flex-ible Algorithms for Image Registration) software package.

Harald KoestlerUniversity of Erlangen-Nurembergharald.koestler@informatik.uni-erlangen.de

MS30

Numerical Geometry of Non-Rigid Shapes

Non-rigid shapes are ubiquitous in the world surroundingus, at all levels from micro to macro. The need to studysuch shapes and model their behavior arises in the fieldsof computer vision, pattern recognition, and graphics in awide spectrum of applications ranging from medical imag-ing to security. The tutorial is a self-contained compre-hensive introduction to analysis and synthesis of non-rigidshapes, with a good balance between theory, numeric meth-ods, and applications. One of the main emphases will beon practical methods. Examples of applications from com-puter vision and pattern recognition, computer graphics,and geometry processing will be shown.

Alex BronsteinDepartment of Computer ScienceTechnion - Israel Institute of Technology

bron@cs.technion.ac.il

Michael BronsteinEE Dept. Technion Israelmbron@tx.technion.ac.il

Ron KimmelTechnion, Haifa, Israelron@cs.technion.ac.il

MS31

Exemplar-based Inpainting from a VariationalPoint of View

Among all methods for reconstructing missing regions ina digital image, the so-called exemplar-based algorithmsare very efficient and often produce striking results. Theyare based on the simple idea – initially used for texturesynthesis – that the unknown part of an image can bereconstructed by simply copying samples extracted fromthe known part. Many variants have been proposed whoseperformances vary according to the type of image. Be-yond heuristic considerations, very little has been done inthe literature to explain the performances of this class ofalgorithms from a theoretical point of view. With a par-ticular focus on the ability to reconstruct the geometry,we discuss in this paper a variational interpretation in RN

of these methods. We propose an optimization model andseveral variants, and prove the existence of minimizers inthe framework of functions of bounded variation. Focus-ing on a simple 2D situation, we provide experimental ev-idences that these global variational models are more effi-cient than a basic patch-based algorithm for reconstructingcertain long-range geometric features without any loss ofquality for the texture reconstruction. We eventually pro-pose additional variants that fulfill a couple of axiomaticrequirements and have a better asymptotic behaviour asthe patch size goes to zero. This is a joint work with Si-mon Masnou and Said Ladjal. This work has been donewith the support of the French “Agence Nationale de laRecherche” (ANR) under grant Freedom (ANR07-JCJC-0048-01).

Jean-Francois AujolCMLA, ENS Cachan, CNRS, UniverSudaujol@cmla.ens-cachan.fr

Saıd LadjalTelecom ParisTechladjal@enst.fr

Simon MasnouUniversite Paris 6masnou@ann.jussieu.fr

MS31

MRI Superresolution Using High ResolutionAnatomical Priors

In Magnetic Resonance Imaging low-resolution images areroutinely interpolated to decrease voxel size and improveapparent resolution. However, classical interpolation tech-niques are not able to recover the high frequency informa-tion lost during the acquisition process. In the present pa-per a new superresolution method is proposed to recoversuch information using coplanar high resolution images.The proposed methodology takes benefit from the fact thatin typical clinical settings both high and low-resolution im-

IS10 Abstracts 73

ages of different types are taken from the same subject.These available high resolution images can be used to im-prove effectively the resolution of other coplanar lower res-olution images. Experiments on synthetic and real dataare supplied to show the effectiveness of the proposed ap-proach. A comparison with classical interpolation tech-niques is presented to demonstrate the improved perfor-mance of the proposed methodology over previous State-of-the-art methods.

Antoni BuadesParis Descartestoni.buades@uib.es

MS31

Image Denoising with Nonlocal Spectral GraphWavelets

We present a new method for denoising photographic im-ages based on a novel nonlocal spectral graph wavelettransform. We employ the transform formed using thegraph Laplacian corresponding to a nonlocal image graphmeasuring similarities between image regions, yieldingwavelets at multiple scales with the interesting propertythat they diffuse among regions of similar image content.Denoising by soft thresholding with threshold determinedfrom a simple Laplacian model for the clean coefficientsyields good results.

David HammondEPFLdavid.hammond@epfl.ch

Karthik RaoaroorEcole Polytechnique Federale de Lausannekarthik.raoaroor@epfl.ch

Laurent JacquesUniversite Catholique de Louvainlaurent.jacques@uclouvain.be

Pierre VandergheynstEcole Polytechnique Federale de Lausannepierre.vandergheynst@epfl.ch

MS31

Neighborhod Filters and Novel Bayesian Approxi-mations for Non-local Image Regularization

In this talk, I will present formal connections betweennon-parametric estimation approaches, neighborhood fil-ters and block estimators in the Bayesian framework. Iwill provide a statistical interpretation to current patch-based methods and justify the Bayesian inference thatneeds to explicitly accounts for discrepancies between themodel and the data. I will present a recent method recom-mended in situations where the posterior or the likelihoodare intractable or too prohibitive to calculate. In particu-lar, the proposed approximations are suited for the analy-sis of large-dimensional distribution of patches and enableto denoise images corrupted by non-Gaussian noises. Wedemonstrate our algorithms on both artificial and real ex-amples.

Charles KervrannINRIA Rennes - Bretagne Atlantique / MIA - INRARennes, Franceckervran@irisa.fr

MS31

Modeling Locally Parellel Textures

In this talk I will present a new adaptive framework forlocally parallel texture modeling. Oscillating patterns aremodeled with functionals that constrain the local Fourierdecomposition of the texture. We introduce a first convextexture functional which is a weighted Hilbert norm. Theweights on the local Fourier atoms are optimized to matchthe local orientation and frequency of the texture. Thisadaptive convex model is then used to solve inverse prob-lems in image processing, such as image decomposition andinpainting. The local texture orientation and frequency ofthe texture component are adaptively estimated during theminimization process. Furthermore, in the inpainting case,convex models present the issue of attenuation inside largemissing parts. The amplitude of the reconstructed oscil-lating patterns tends indeed to vanish inside large holes.To deal with this difficult problem, a non convex general-ization of our model is designed. This new model enablesto impose the amplitude of the oscillating patterns insidethe reconstructed parts and to cope with the inpainting ofgeneral oscillations profiles. Numerical results show thatour method improves state of the art algorithms for direc-tional textures. This is a joint work with Pierre Maureland Jean-Francois Aujol.

Gabriel PeyreCeremade, Universite Paris Dauphinegabriel.peyre@ceremade.dauphine.fr

Pierre MaurelIRISApierre.maurel@normalesup.org

Jean-Fancois AujolCMLA, ENS de Cachanaujol@cmla.ens-cachan.fr

MS32

Scales Coming from K-functionals

In image decomposition, an image f is decomposed intou+v, where u and v are in some function spaces X and Yrespectively. This can be seen as viewing f to belong to aninterpolating space between X and Y. Given the choicesfor X and Y, we will discuss and analyze the choice for thisinterpolating space, which provides us with an automaticdecomposition of f.

Triet LeDepartment of Mathematics, Yale Universitytrit.le@yale.edu

MS32

Edge-enhanced Image Reconstruction Using TotalVariation Norm and High-order Edge-preservingUp-sampling Operators

We have introduced an image resolution enhancementmethod for multidimensional images based on a variationalapproach that uses the total variation norm as regulariz-ing functional. Given an appropriate down-sampling oper-ator, the reconstruction problem is posed using a decon-volution model under the assumption of Gaussian noise.In this research work we explore different edge-preservingup-sampling operators with different orders of spatial ac-curacy. The operators are defined using nonlinear localfunctions to preserve edges automatically when they are

74 IS10 Abstracts

present. We analyze the behavior and robustness of thoseoperators under noisy data. Numerical results are pre-sented using those operators in conjunction with our vari-ational model for image enhancement.

Antonio MarquinaUniversity of Valencia, Spainmarquina@math.ucla.edu

Shantanu JoshiLONI, UCLAsjoshi@loni.ucla.edu

Stanley J. OsherMathematics, UCLAsjo@math.ucla.edu

Ivo D. DinovUCLACenter for Computational Biologyivo.dinov@loni.ucla.edu

Jack Van HornLONI, UCLAjack.vanhorn@loni.ucla.edu

MS32

Fast TV based Segmentation and Surface Interpo-lation

Variational globally convex segmentation results involvingtotal variation minimization have been devised in recentyears by Chan, Esedoglu and Nikolova, for segmentationand by Chambolle for geometric motion. These can be usedfor classical geometric problems in vision, however theywere believed to be slow to implement. Recently developedfast algorithms involving Bregman methods turn out to bevery effective for these problems. We’ll descibe progress inthis area.

Tom GoldsteinMathematics, UCLAtagoldst at math.ucla.edu

Xavier BressonUCLADepartment of Mathematicsxbresson@math.ucla.edu

Jian YeMathematics, UCLAye@math.ucla.edu

Stanley J. OsherUniversity of CaliforniaDepartment of Mathematicssjo@math.ucla.edu

MS32

Nonlinear Iterative Algorithms for Total VariationDenoising and Deblurring

We propose nonlinear Jacobi and Gauss-Seidel iterativeprocedures for approximating the solution of the Euler-Lagrange equations associated to the TV minimizationdenoising and deblurring problems. The algorithms areformulated from a suitable discretization of the Euler-Lagrange equation associated to the specific variational

problem. The iteration functions are constructed as a non-linear convex combination of neighboring values allowingthe solution to satisfy a maximum principle. We proposea specific stopping criterion that allows convergence in afinite number of iterations. We present numerical exam-ples of two-dimensional denoising and deblurring-denoisingproblems.

Suzana SernaDeparment of Mathematics, UCLAserna@math.ucla.edu

Antonio MarquinaUniversity of Valencia, Spainmarquina@math.ucla.edu

Stanley J. OsherUniversity of CaliforniaDepartment of Mathematicssjo@math.ucla.edu

MS33

Convex Formulation and Exact Global Solutionsfor Multi-phase Piecewise Constant Mumford-Shah Image Segmentation

Most variational models for multi-phase image segmenta-tion are non-convex and possess multiple local minima,which makes solving for a global solution an extremely diffi-cult task. In this work, we provide a method for computinga global solution for the (non-convex) multi-phase piece-wise constant Mumford-Shah (spatially continuous Potts)image segmentation problem. Our approach is based onusing a specific representation of the problem due to Lie etal. We then establish an augmented Lagrangian methodto reduce the problem to a sequence of non-convex mini-mization problems, each of which can globally solved usinga convexification technique due to Pock et al. Unlike somerecent methods in this direction, our method can guaranteethat a global solution is obtained. We believe our methodto be the first in the literature that can make this claim.

Ethan BrownDepartment of MathematicsUniversity of California at Los Angelesethan@math.ucla.edu

Tony ChanUniversity of California. Los Angeleschan@math.ucla.edu

Xavier BressonUCLADepartment of Mathematicsxbresson@math.ucla.edu

MS33

Local Scales in Images

We propose a linear approach to extract local scales ofoscillatory patterns in images in a multi-scale fashion. Wewill discuss the relation of local scales to the theory offunction spaces and the extension to nontangential localscales and non-linear evolution equations.

Peter JonesYale Universityjones@math.yale.edu

IS10 Abstracts 75

Triet LeDepartment of Mathematics, Yale Universitytriet.le@yale.edu

MS33

A Variational Model for Infinite Perimeter Seg-mentations Based on Lipschitz Level Set Func-tions: Denoising While Keeping Finely OscillatoryBoundaries

We propose a new model for segmenting piecewise con-stant images with irregular object boundaries: a variant ofthe Chan-Vese model, where the length penalization of theboundaries is replaced by the area of their neighborhood ofthickness ε. Our aim is to keep fine details and irregular-ities of the boundaries while denoising additive Gaussiannoise. For the numerical computation we revisit the classi-cal BV level set formulation considering suitable Lipschitzlevel set functions instead of BV ones.

Marcello PonsiglioneDipartimento di MatematicaUniversita‘ di Roma Iponsigli@mat.uniroma1.it

Marco BarchiesiBCAM, Bizkaia Technology Park, Building 500, 48160Derio, Spbarchiesi@bcamath.org

Sung Ha KangGeorgia Inst. of TechnologyMathematicskang@math.gatech.edu

Triet M. LeYale Universitytriet.le@yale.edu

Massimiliano MoriniSISSATrieste,Italymorini@sissa.it

MS33

Adapted Local Scales and Smoothness, and NL-means

The NL-means algorithm and its cousins represent a gray-scale image not as a function of R2, but as a function ofthe set of patches of the image. On this set of patches,the algorithm simply becomes a linear diffusion, with thestandard associated scale space. I will discuss why thispoint of view is useful and give examples from image andaudio analysis.

Arthur SzlamDepartment of MathematicsNYUaszlam@courant.nyu.edu

MS34

Optimization with Total Generalized VariationPenalty

In the talk, we focus on the solution of minimization prob-lems involving a total generalized variation penalty term.Total generalized variation is a novel nonsmooth concept

which involves and balances derivatives up to a certain or-der. Applied to mathematical imaging, it usually leads tononsmooth and nonconvex minimization problems. Theirnumerical solution is discussed and examples are presented,showing in particular the absence of staircasing effects forthis approach.

Kristian BrediesUniversitat GrazInstitute of Mathematics and Scientific Computingkristian.bredies@uni-graz.at

MS34

DC Programming Approaches for Image Restora-tion and Image Segmentation

We present an efficient approach in nonconvex nonsmoothprogramming called DC (Difference of Convex functions)programming and DC algorithms (DCA) for two classesof problems in image processing: the image restorationby globally minimizing the Gibbs energy function via aMarkov random field model, and the image segmentationvia Fuzzy C-Means (FCM) clustering model. Experimentalresults on noisy images have illustrated the effectiveness ofthe proposed algorithm and its superiority with respect tothe standard GNC algorithm (for image restoration) andFCM algorithm (for image segmentation).

Hoai An Le ThiUniversite Paul Verlaine, Reims, Francelethi@univ-metz.fr

MS34

DC (Difference of Convex functions) Programmingand DCA (DC Algorithms) for Smooth/ Nons-mooth Nonconvex Programming

The DC programming and DCA address the problem ofminimizing a function f = g−h , (g, h being lower semicon-tinuous proper convex functions on the Euclidean space) ona closed convex set. The DCA, based on local optimalityconditions and DC duality, has been successfully appliedto a lot of different and various smooth/nonsmooth non-convex programs. Moreover it has quite often given globalsolutions and proved to be more robust and more efficientthan related standard methods, especially in the large-scalesetting.

Tao Pham DinhLaboratory of Modeling, Optimization and OperationsResearchNational Institute for Applied Sciences -Rouen, Francepham@insa-rouen.fr

MS34

Linear Convergence Method for a Non-convexVariational Model

In this talk, we consider a non-convex variational model.We propose to use strictly convex optimization models toapproximate the non-convex functional. We show that thesolutions of these strictly convex optimization models willconverge to the global minimizer of the original non-convexfunctional. We show that the solution of the strictly convexoptimization model can be determined by using an itera-tive algorithm, and the convergence rate is linear. Numer-ical examples are presented to show the efficiency of the

76 IS10 Abstracts

proposed method.

Tieyong ZengDepartment of MathematicsHong Kong Baptist Universityzeng@hkbu.edu.hk

Michael NgHong Kong Baptist UniversityDepartment of Mathematicsmng@math.hkbu.edu.hk

MS35

Synthetic Aperture Radar Imaging with MotionEstimation and Autofocus

We introduce from first principles a synthetic apertureradar (SAR) imaging and motion estimation methodthat is combined with radar platform trajectory estima-tion. This method segments the data into properly cali-brated small apertures and uses space-time phase methods(Wigner transforms and ambiguity functions) to estimatetarget motion and trajectory perturbations. X-band per-sistent surveillance SAR is a specific application that iscovered by our analysis. This is joint work with ThomasCallaghan and George Papanicolaou.

Liliana BorceaRice UniversityDept Computational & Appl Mathborcea@caam.rice.edu

MS35

Transmission Eigenvalues and Their Application inInverse Scattering Theory

We consider the scattering problem for an inhomogeneousmedium and discuss a new related eigenvalue problemknown as the interior transmission eigenvalue problem. Wefirst prove that there exists a countable set of transmis-sion eigenvalues and then show that these eigenvalues canbe determined from the far field data. Finally, we obtainFaber-Krahn type inequalities for transmission eigenvalueswhich, if D is known, provide lower and upper bounds onthe index of refraction n(x).

Fioralba CakoniUniversity of Delawarecakoni@math.udel.edu

MS35

Direct and Inverse Obstacle Scattering Over RoughSurfaces

We develop a theory for direct obstacle scattering of ob-stacles over a rough surface. Using that theory, we addressthe inverse obstacle scattering problem in which measure-ments of the wave field are collected on a planar arrayover a spectrum of wavelengths. For applications in singlemolecule detection and characterization, we seek to recoverthe number and locations of the scatterers as well as eachof their spectral properties.

Arnold D. KimUniversity of California, Mercedadkim@ucmerced.edu

MS35

Passive Imaging Using Distributed Apertures inMulti-path Environments

We present a new passive image formation method capableof exploiting information about multi-path scattering inthe environment using measurements from a sparse array ofreceivers that rely on illumination sources of opportunity.We use a statistical and physics-based approach to modelmulti-path propagation and formulate the imaging problemas a spatially resolved binary hypothesis testing problem.Our imaging method is applicable in the presence of bothcooperative and non-cooperative sources of opportunity.

Birsen YaziciDepartment of Electrical, Computer and SystemsEngineeringRensselaer Polytechnic Instituteyazici@ecse.rpi.edu

MS36

Statistical Methods for Manifold Learning

It has recently been recognized that if the signal of interestto an inverse problem is known to reside on a manifold,the number of required measurements needed for accurateinference may be reduced substantially. This is closely re-lated to the new field of compressive sensing (CS). In thistalk we discuss development of new nonparametric statis-tical methods to learn the statistical properties of a low-dimensional manifold. We show how this technique maybe employed in several applications, including CS.

Lawrence CarinDuke UniversityDept of Electrical & Computer Engineeringlcarin@ee.duke.edu

MS36

Bayesian Hypermodels in Medical Imaging

In this talk, we review the hierarchical Bayesian models inmedical applications. In the literature, it has been demon-strated in the context of machine learning and in imageprocessing that Bayesian hierarchical model provide a flex-ible framework for implementing a priori information suchas sparsity of the image or its gradient, and the interestin compressed sensing has increased the need to work outfurther the possibilities of hierarchical models. We discussvarious medical imaging applications where the hierarchi-cal models turn out to be useful and improve the qualityof the reconstructions.

Erkki Somersalo, Daniela CalvettiCase Western Reserve Universityerkki.somersalo@case.edu, dxc57@case.edu

MS36

Using Learning and Posterior Modeling to SegmentImages

This talk proposes a direct posterior modeling methodol-ogy for segmenting images. The methodology provides acanonical way of using machine-learning techniques, suchas kernel-based methods, in a level-set segmentation. Oneadvantage of this approach is that it is possible to learnto segment complex images, such as ultrasound images,which have significant spatial inhomogeneity. This talkwill present the methodology as well experimental results

IS10 Abstracts 77

of using the posterior modeling technique.

Hemant TagareYale Universityhemant.tagare@yale.edu

MS36

Expectation-Maximization Algorithm with LocalAdaptivity for Image Analysis

In this work we develop an Expectation-Maximization(EM) algorithm with local adaptivity that can combineglobal statistics, local statistics, and and geometric infor-mation. In particular we apply our algorithm to imagesegmentation and classification. The key idea is to cou-ple global statistics extracted from proper statistic modelwith local statistical and geometrical information. Thesecombined information are used to design an adaptive localclassification strategy that can both improve robustnessand keep fine features.

Hongkai ZhaoUniversity of California, IrvineDepartment of Mathematicszhao@math.uci.edu

Shingyu LeungHong Kong University of Science and Technologymasyleung@ust.hk

Gang LiangIndustrygumpleon@gmail.com

Knut SolnaUniversity of California at Irvineksolna@math.uci.edu

MS37

Pan Sharpening and Multimodal Data Fusion inRemote Sensing Applications

There has been significant research on pan-sharpening mul-tispectral imagery with a high resolution image, but therehas been little work extending the procedure to high dimen-sional hyperspectral imagery. We present a wavelet-basedvariational method for fusing a high resolution image anda hyperspectral image with an arbitrary number of bands.To ensure that the fused image can be used for tasks such asclassification and detection, we explicitly enforce spectralcoherence in the fusion process. This procedure producesimages with both high spatial and spectral quality. Wedemonstrate this procedure on several AVIRIS and HY-DICE images.

Andrea L. BertozziUCLA Department of Mathematicsbertozzi@math.ucla.edu

MS37

Dictionary Learning Methods for HyperspectralImage Classification

We investigate the application of sparse reconstruction anddictionary learning methods to hyperspectral image anal-ysis. After training dictionaries for specific classes, weclassify unknown pixels by comparing reconstruction er-rors across the different class dictionaries. We also discuss

a novel method for the pixel unmixing problem that yieldssparse abundance vectors.

John GreerNational Geospatial-Intelligence Agencyjohn.b.greer@nga.mil

MS37

Unsupervised Clustering of High Dimensional Sub-spaces

A clustering framework within the sparse modeling anddictionary learning setting is introduced in this work. Weoptimize for a set of dictionaries for which the signals arebest reconstructed in a sparse coding manner (subspaces).The proposed clustering uses a novel measurement for thequality of the sparse representation. We illustrate state-of-the-art results for supervised classification and unsuper-vised clustering on standard standard datasets and textureimages.

Guillermo SapiroUniversity of MinnesotaDept Electrical & Computer Engineeringguille@umn.edu

MS37

Multiscale Representations for Point Cloud Data

We shall describe a progressive encoder for Lidar pointcloud data based on local PCA, adaptive partitioning,Hausdorff distance, and implicit representation of the pointcloud surface. This encoder has as its goal best distortionin the Hausdorff metric for a given bit budget. Applica-tions of the encoder will be given for point cloud data.The encoder is designed to handle noisy data by utilizinglearning theory for the Hausdorff metric.

Andrew WatersRice Universityandrew.e.waters@rice.edu

MS38

Data Reduction Methods for Optical Tomographyof Large DataSets

A current topic in Optical Tomography is the acquisition ofdata using camera detectors. The data can be obtained ina rotating scanning geometry and can include time resolveddata, leading to large 4 or 5 dimensional data sets of sizeup to 108 − 1010. Due to the inherent low resolution ofthe method (stemming from its severe ill-posedness) muchof this data is redundant. In this talk we consider somemetohds for compressing the information content in thesedata sets and the commensurate improvement in imagereconstruction performance.

Simon ArridgeUniversity College LondonS.Arridge@cs.ucl.ac.uk

MS38

Approximation Errors and Model Reduction in 3DDiffuse Optical Tomography

Model reduction is often required in diffuse optical tomog-raphy (DOT), typically due to limited available computa-tion time or computer memory. In practice, this means

78 IS10 Abstracts

that one is bound to use coarse mesh and truncated com-putation domain in the model for the forward problem. Inthis talk we apply the Bayesian approximation error modelfor the compensation of modeling errors caused by domaintruncation and a coarse computation mesh in DOT. Theapproach is tested using experimental data. The resultsshow that when the approximation error model is em-ployed, it is possible to use mesh densities and computationdomains that would be unacceptable with a conventionalmeasurement error model.

Ville P. KolehmainenDepartment of PhysicsUniversity of KuopioVille.Kolehmainen@uku.fi

MS38

Optical Tomography with the DiscontinuousGalerkin Method

We present a discontinuous Galerkin (DG) formulation ofthe diffusion equation to tackle the meshing issues asso-ciated with finite element formulations. DG method hasalso been employed to solve the diffusion equation on amulti-layered highly diffusive domain with refractive indexmismatch between consecutive layers. Numerical studiesare presented for the forward problem and reconstructionsemploying DG method on both experimental and simu-lated data. These results show that DG formulations areas accurate as finite element formulations and are betterequipped to tackle discontinuities in the solution.

Surya Prerapa, Simon ArridgeUniversity College Londons.prerapa@cs.ucl.ac.uk, S.Arridge@cs.ucl.ac.uk

MS38

Numerical Solutions of Inverse Transport Problemswith Interior Data for Imaging Applications

Inverse problems related to the linear radiative transportequation find applications in medical imaging such as op-tical tomography and optical molecular imaging. In tran-ditional optical tomography, the data used for imaging areonly collected on the boundary of the imaging domain. Weconsider in this talk some inverse transport problems wherewe can collect interior data. We will present some numer-ical algorithms as well as some reconstructions with syn-thetic interior data.

Kui RenUniversity of Texasren@math.utexas.edu

MS39

Integro Differential Equation Schemes Based on(BV, L1) Decomposition

The hierarchical multiscale image representation of Tad-mor, Nezzar and Vese, gives rise to an integro-differentialequation (IDE) for a multiscale image representation. Onecan obtain a similar IDE using (BV,L1) multiscale hierar-chical decomposition. To this end, one integrates in inversescale space a succession of refined, recursive ‘slices’ of theimage, which are balanced by a typical curvature term atthe finer scale. Once the IDE is obtained we can mod-ify it based on our image processing needs. We will discussvarious (BV, L1) IDE schemes incorporating filtering, edgeenhancing and deblurring. We will also examine qualitative

differences between (BV, L1) and (BV,L2) IDE schemes.

Prashant AthavaleIPAM, UCLAprashant@math.ucla.edu

Eitan TadmorUniversity of MarylandUSAtadmor@cscamm.umd.edu

MS39

Modeling Locally Parallel Oscillating Patterns

Since the seminal work by Y. Meyer in 2001, image de-composition into geometry + texture has drawn a lot ofattention. In particular, it was shown by Osher-Sole-Vese,and later by Aujol-Gilboa, that using a Hilbert space tomodel texture is quite effective. In this work, we extendthese ideas to build a spatially adaptive texture norm. Ex-periments in image decomposition and in image inpaint-ing are shown to validate the approach. This work hasbeen supported by the French ”Agence Nationale de laRecherche” (ANR), under grant NATIMAGES (ANR-08-EMER-009) ”Adaptivity for natural images and texturerepresentations”.

Jean-Francois AujolCMLA, ENS Cachan, CNRS, UniverSudaujol@cmla.ens-cachan.fr

Pierre MaurelIRISApierre.maurel@normalesup.org

Gabriel PeyreCeremade, Universite Paris Dauphinegabriel.peyre@ceremade.dauphine.fr

MS39

Fast Gradient-Based Schemes for Total VariationMinimization

We present fast gradient-based schemes for image denoisingand deblurring problems based on the discretized total vari-ation (TV) minimization model with constraints. Our ap-proach relies on combining a novel monotone version of thefast iterative shrinkage/ thresholding algorithm (FISTA)we recently introduced, with the well known dual approachto the denoising problem. We derive a fast algorithm forthe constrained TV-based image deblurring problem. Theproposed scheme is remarkably simple and is proven toexhibit a global rate of convergence which is significantlybetter than currently known gradient based methods. Ourresults are applicable to both the anisotropic and isotropicdiscretized TV functionals. Initial numerical results con-firm the predicted underlying theoretical convergence rateresults, and demonstrate the viability and efficiency of theproposed algorithms on image deblurring problems withbox constraints. This talk is based on a joint work withMarc Teboulle.

Amir BeckFaculty of Industrial Engineering and ManagementTECHNION - Israel Institute of technologybecka@ie.technion.ac.il

IS10 Abstracts 79

MS39

Inverse Free-discontinuity Problems and IterativeThresholding Algorithms

Free-discontinuity problems describe situations where thesolution of interest is defined by a function and a lower di-mensional set consisting of the discontinuities of the func-tion. Hence, the derivative of the solution is assumed to bea ”small function” almost everywhere except on sets whereit concentrates as a singular measure. This is the case,for instance, in certain digital image segmentation prob-lems. 1) In presence of an inverse problem, no existenceresults were available so far. First of all we show prelimi-nary new results on the existence of minimizers for inversefree-discontinuity problems, by restricting the solutions toa class of functions which we called the Rondi’s class. 2)If we discretize such situations for numerical purposes, theinverse free-discontinuity problem in the discrete settingcan be re-formulated as that of finding a derivative vectorwith small components at all but a few entries that ex-ceed a certain threshold. This problem is similar to thoseencountered in the field of ”sparse recovery”, where vec-tors with a small number of dominating components inabsolute value are recovered from a few given linear mea-surements via the minimization of related energy function-als. As a second result, we show that the computationof global minimizers in the discrete setting is an NP-hardproblem. 3) With the aim of formulating efficient com-putational approaches in such a complicated situation, weaddress iterative thresholding algorithms that intertwinegradient-type iterations with thresholding steps which weredesigned to recover sparse solutions. It is natural to wonderhow such algorithms can be used towards solving discretefree-discontinuity problems. This talk explores also thisconnection, and, by establishing an iterative thresholdingalgorithm for discrete inverse free-discontinuity problems,provides new insights on properties of minimizing solutionsthereof. This is partially a joint work with Riccardo March(CNR, Italy) and Rachel Ward (Courant Institute, NYU,USA).

Massimo FornasierJohann Radon Institute for Computational and AppliedMathematics (RICAM)massimo.fornasier@oeaw.ac.at

MS40

ShapeGoogle: Geometric Words and Expressionsfor Invariant Shape Retrieval

Large databases of 3D models available in public domainhave created the demand for shape search and retrieval al-gorithms capable of finding similar shapes in the same waya search engine responds to text quires. Since many shapesmanifest rich variability, shape retrieval is often requiredto be invariant to different classes of transformations andshape variations. One of the most challenging settings inthe case of non-rigid shapes, in which the class of trans-formations may be very wide due to the capability of suchshapes to bend and assume different forms. In this talk, wewill apply modern methods in computer vision to problemsof non-rigid shape analysis. Feature-based representationsuch as the Scale-Invariant Feature Transform (SIFT) andmetric learning methods have recently gained popularityin computer vision, while remaining largely unknown inthe shape analysis community. We will show analogousapproaches in the 3D world applied to the problem of non-rigid shape retrieval in large (potentially Internet-scale)databases. This will allow us to adopt methods employed

in search engines for efficient indexing and search of shapes.

Alex Bronstein, Michael BronsteinDepartment of Computer ScienceTechnion - Israel Institute of Technologybron@cs.technion.ac.il, mbron@cs.technion.ac.il

Maks Ovsjanikov, Leonidas GuibasStanford Universitymaks@stanford.edu, guibas@cs.stanford.edu

MS40

Exploiting BoW Paradigm for 3D Shape Descrip-tion and Matching

The Bag of Words (BoW) paradigm has been introducedoriginally for natural language processing and it has beensuccessfully applied in several other domains. For instancein Computer Vision the BoW approach has been proposedfor object categorization, image retrieval and human actionrecognition. Here, we show the effectiveness of the BoWonto the 3D domain by exploiting both i) region-based, andii) point-based techniques to characterize local parts of a3D shape. Region-based approaches build the visual vocab-ulary starting from the regions extracted by a 3D objectsegmentation process. Point-based techniques are insteadoriented to the detection of few feature points from the 3Dsurface. Moreover, we show how the spatial relations be-tween object subparts can be easily encoded by combiningthe BoW paradigm with shape context (i.e., local descrip-tors and global context). Several experiments are reportedon different applications namely object retrieval and cate-gorization, point-to-point matching, and 3D partial viewsregistration.

Umberto CastellaniUniversity of Veronaumberto.castellani@univr.it

MS40

Geodesic Shape Retrieval with Optimal Transport

In this talk, I will review several geodesic representationsfor shapes and surfaces, and their use for retrieval with in-variance to bendings and articulations. I will present a newfamilly of high dimensional geodesic shape signatures, thatextend several previous proposals. These new geodesic rep-resentations take into account the interplay between severalgeodesic caracteristics. It is defined as high dimensionalhistograms of several key geodesic features, that detectglobal caracteristics of shapes and surfaces. The retrivalis performed with a nearest neighbor query according tothe Wasserstein distance between these multi-dimensionalsignatures. The search is performed with a fast approxi-mated optimal transport algorithm. This a joint work withJulien Rabin and Laurent Cohen.

Laurent D. CohenCNRS, UMR 7534Universite Paris-Dauphine, CEREMADEcohen@ceremade.dauphine.fr

Gabriel PeyreUniversite Paris-Dauphinegabriel.peyre@ceremade.dauphine.fr

Julien RabinTelecom ParisTechjulien.rabin@telecom-paristech.fr

80 IS10 Abstracts

MS40

Surface Feature Detection and Description withApplications to Mesh Matching

We revisit local feature detectors/descriptors developed for2D images and extend them to the more general frame-work of scalar fields defined on 2D manifolds. We providemethods and tools to detect and describe features on sur-faces equiped with scalar functions, such as photometricinformation. This is motivated by the growing need formatching and tracking photometric surfaces over temporalsequences, due to recent advancements in multiple cam-era 3D reconstruction. We propose a 3D feature detector(MeshDOG) and a 3D feature descriptor (MeshHOG) foruniformly triangulated meshes, invariant to changes in ro-tation, translation, and scale. The descriptor is able to cap-ture the local geometric and/or photometric properties ina succinct fashion. Moreover, the method is defined gener-ically for any scalar function, e.g., local curvature. Resultswith matching rigid and non-rigid meshes demonstrate theinterest of the proposed framework.

Radu HoraudINRIA GrenobleRadu.Horaud@inrialpes.fr

Andrei ZaharescuAimetis Incandrei.zaharescu@aimetis.com

Edmond BoyerINRIA Grenobleedmond.boyer@inrialpes.fr

MS41

Elasticity in Image Registration Revisited

We present a general hyperelasticity regularization frame-work for image registration. The framework is demon-strated on a number of synthetic and real image registra-tion applications.

Mads F. Hansen, Rasmus LarsenDTU Informaticsmfh@imm.dtu.dk, rl@imm.dtu.dk

MS41

On Multiple Level-set Regularization Methods forInverse Problems

We analyze a multiple level-set method for solving inverseproblems with piecewise constant solutions. This methodcorresponds to an iterated Tikhonov method for a particu-lar Tikhonov functional based on TV-H1 penalization. Wedefine generalized minimizers for our Tikhonov functionaland establish an existence result. Moreover, we prove con-vergence and stability results of the proposed Tikhonovmethod. A multiple level-set algorithm is derived fromthe first-order optimality conditions for the Tikhonov func-tional, similarly as the iterated Tikhonov method. Theproposed multiple level-set method is tested on an inversepotential problem. Numerical experiments show that themethod is able to recover multiple objects as well as mul-tiple contrast levels. This is a joint work with A DeCezaroand A Leitao.

Xue-cheng TaiDept. of Mathematics, University of Bergen, Norway andDiv. of Math. Sciences, Nanyang Tech. University

tai@mi.uib.no

MS41

Image Registration and Segmentation Using a Non-linear Elasticity Smoother

We present a new non-parametricregistration-segmentation method. The problem is cast asan optimization one, combining a matching criterion basedon the active contour without edges for segmentation, anda nonlinear-elasticity-based smoother on the displacementvector field. This modeling is twofold: first, registration isjointly performed with segmentation since guided by thesegmentation process; it means that the algorithm pro-duces both a smooth mapping between the two shapes andthe segmentation of the object contained in the referenceimage. Secondly, the use of a nonlinearelasticity-type reg-ularizer allows large deformations to occur, which makesthe model comparable in this point with the viscous fluidregistration method. Several applications are proposed todemonstrate the potential of this method to both segmen-tation of one single image and to registration between twoimages.

Carole Le GuyaderINSA Rouen, Francecarole.le-guyader@insa-rouen.fr

Luminita A. VeseUniversity of California, Los AngelesDepartment of Mathematicslvese@math.ucla.edu

MS41

Continuous Models for Rigid and Nonrigid Regis-tration

We will present a robust continuous mutual informationmodel for multimodality registration. The probability andjoint probability density functions for the continuous im-ages are defined analytically. This model leads to a smoothmutual information which does not have the typical inter-polation artifacts, resulting in much higher success rates.Moreover, we will propose a nonrigid registration modelformulated in a particle framework. Our model can accom-modate both small and large deformations, with sharperedges and clearer texture achieved at less computationalcost. Numerical results on a variety of images are pre-sented.

Justin WanUniversity of WaterlooDepartment of Computer Sciencejwlwan@uwaterloo.ca

Zhao YiUCLAzyi@ucla.edu

Lin Xu, Tiantian BianUniversity of Waterlool8xu@uwaterloo.ca, tbian@uwaterloo.ca

MS42

Inverse Scattering by Compressed Sensing

Inverse scattering problem is analyzed from the perspec-tive of compressed sensing. It is shown that with appro-

IS10 Abstracts 81

priately designed bases and sampling methods the numberof measurements/sensors can be significantly reduced incomparison to traditional methods.

Albert C. FannjiangDepartment of MathematicsUniversity of California at Daviscafannjiang@ucdavis.edu

MS42

Imaging Localized Scatterers with L1 Optimization

I will give a detailed comparison of resolution and robust-ness for array imaging with L1 and L2 optimization crite-ria, including results from numerical simulations. Joint L1and L2 criteria will also be considered. This is work withAnwei Chai.

George C. PapanicolaouStanford UniversityDepartment of Mathematicspapanico@math.stanford.edu

MS42

Imaging and Detection in Cluttered Media

We consider sensor imaging in a noisy environment by suit-ably migrating the cross correlations of the recorded sig-nals. We analyze the properties of the imaging functionalin the high-frequency regime. We identify the scaling as-sumptions that allow us to image respectively, the supportof random sources and smooth or rough medium variations.

Knut SolnaUniversity of California at Irvineksolna@math.uci.edu

MS42

Data Filtering for Coherent Array Imaging inHeavy Clutter

We consider the problem of coherent array imaging reflec-tors embedded in strongly scattering media. This problemappears in applications such as exploration geophysics andnon-destructive testing of materials. Coherent imaging re-sults in such media are not satisfactory because the coher-ent signal that arrives at the array is too weak. To extendthe applicability range of coherent imaging techniques tostronger scattering environments we propose to performappropriate filtering on the data prior to imaging.

Chrysoula TsogkaUniversity of Crete and FORTH-IACMtsogka@tem.uoc.gr

MS43

Total Variation Methods for 3D Lidar Image De-noising

New imaging capabilities have given rise to higher dimen-sional image processing. This paper presents a generaliza-tion of total variation (TV) based denoising model withspecific application to three-dimensional flash lidar im-agery. The generalization uses a weighted norm, ratherthan the standard Euclidean measure, that accounts forsampling differences that may exist along different axes.We compare this new method against successive two-

dimensional denoising and three-dimensional TV denois-ing.

Frank CrosbyNaval Surface Warfare CenterPanama Cityfrank.crosby@navy.mil

Haomin ZhouGeorgia Institute of TechnologySchool of Mathematicshmzhou@math.gatech.edu

MS43

Visibility Optimization Using Variational Methods

Confined areas, such as those found in littoral regions, re-strict the maneuvering and sensing capabilities of Navalvessels. We introduce a solution to the confined area searchproblem based on the calculus of variations which we im-plement using the level-set framework. The resulting algo-rithm is completely autonomous and can be extended toaccount for: incomplete maps, sensor limitations (range,resolution, etc.), as well as other factors. We also introducean algorithm for positioning n-sensors to achieve maximalcoverage of a confined area.

Rostislav GoroshinNaval Surface Warfare Center - Panama Cityrostislav.goroshin@navy.mil

Haomin ZhouGeorgia Institute of TechnologySchool of Mathematicshmzhou@math.gatech.edu

MS43

Crowd Counting: Modeling Abnormal Events forthe Detection of Suicide Bombers

We present some recent results on the problem of countingthe number of people in a crowded scene. These resultsare obtained with a system for estimating the size of in-homogeneous crowds, composed of pedestrians that travelin different directions, without using explicit object seg-mentation or tracking. First, the crowd is segmented intocomponents of homogeneous motion, using the mixture ofdynamic textures motion model. Second, a set of simpleholistic features is extracted from each segmented region,and the correspondence between features and the numberof people per segment is learned with Gaussian Processregression. We validate both the crowd segmentation thecrowd counting algorithms on hours of video.

Viral Bhalodia, Weixin Li, Nuno VasconcelosUCSDvbhalodi@ucsd.edu, wel017@ucsd.edu, nuno@ece.ucsd.edu

Truong NguyenECE, UCSDnguyent@ece.ucsd.edu

MS43

Object Classification and Identification fromAcoustic Color Images

We introduce a method of enhancing a sonar image withacoustic color. Our method emphasizes the discrimina-

82 IS10 Abstracts

tive properties of the returned spectrum for the purpose ofobject discrimination. This is achieved by analyzing thediscriminating power of different frequency bands and as-sociating the appropriate ones with a color map.

Naoki SaitoUniversity of California, Davisnsaito@ucdavis.edu

Quyen HuynhNaval Surface Warfare Center, Panama Cityquyen.huynh@navy.mil

MS44

Kronecker Compressive Sensing

Compressive sensing (CS) is an emerging approach for ac-quisition of signals having a sparse or compressible repre-sentation in some basis. While the CS literature has mostlyfocused on problems involving 1-D signals and 2-D images,many important applications involve signals that are mul-tidimensional; in this case, CS works best with represen-tations that encapsulate the structure of such signals inevery dimension. We propose the use of Kronecker prod-uct matrices in CS for two purposes. First, we can usesuch matrices as sparsifying bases that jointly model thedifferent types of structure present in the signal. Second,the measurement matrices used in distributed measure-ment settings can be easily expressed as Kronecker prod-uct matrices. The Kronecker product formulation in thesetwo settings enables the derivation of analytical bounds forsparse approximation of multidimensional signals and CSrecovery performance, as well as a means to evaluate noveldistributed measurement schemes.

Marco F. DuartePrinceton Universitymduarte@princeton.edu

Richard G. BaraniukRice UniversityElectrical and Computer Engineering Departmentrichb@rice.edu

MS44

Edge Guided Compressive Imaging Reconstruction

Compressive imaging aims at reconstructing faithful im-ages from a small number of measurements. We strive forsharper images from less measurements through efficientlyusing edge information. Accurate edge detection from un-dersampled data is very challenging due to existence ofubiquitious artifacts and noise. Start with sampled datawith overwhelming small size, the proposed method is twofolded: i) to detect edges from a not-so-perfect first roundreconstruction; ii) to run an edge guided reconstruction.

Weihong GuoDepartment of Mathematics, Case Western ReserveUniversitywxg49@case.edu

Wotao YinRice Universitywotao.yin@rice.edu

MS44

Edge Detection in Blurred Data from Fourier Space

Using Higher-Order Edge Detectors

A novel approach is presented that allows the detectionof edges in piece wise smooth signals from partial Fourierdata. Detection of edges has many important applicatione.g. in medical image analysis or image reconstruction.Our approach combines a method to find jump discontinu-ities in Fourier data and ideas from compressed sensing. Itis able to detect edges in Fourier data without the presenceof ringing artifacts common to higher order edge detectionmethods.

Wolfgang StefanRice Universitywolfgang.stefan@rice.edu

Aditya ViswanathanArizona State Universityaditya.v@asu.edu

Anne GelbMathematics DepartmentArizona State Universityag@harvey.la.asu.edu

Rosemary RenautArizona State Universityrosie.renaut@asu.edu

MS44

Compressive Sensing via Iterative Support Detec-tion

We present a new compressive sensing reconstructionmethod “ISD’, aiming to achieve fast reconstruction anda reduced requirement on the number of measurementscompared to the classical �1 minimization approach. ISDaddresses failed cases of �1–based construction due to in-sufficient measurements, in which the returned signals arenot equal or even close to the true signals. Specifically,given an incorrect signal, ISD detects an index set I thatincludes components most likely to be true nonzeros andsolves min{∑

i�∈I|xi| : Ax = b} for a new signal x, and it

iterates these two steps alternatively using latest x and Ifrom one another until convergence.

Yilun WangCornell Universityyilun.wang@gmail.com

Wotao YinRice Universitywotao.yin@rice.edu

MS44

Effective Compressive Sensing with Toeplitz andCirculant Matrices

Compressive sensing requires a small number of incoher-ent measurements of the unknown signal as the input. Toachieve the co-incoherence, random linear projections areoften among the best choices. However, they are difficult toimplement physically or the implementation would causea prohibitive overhead. We describe how random Toeplitzand circulant matrices can be easily (or even naturally) re-alized in various imaging applications and introduce fastalgorithms for their corresponding signal reconstructionproblems. Results show that they are not only as effec-

IS10 Abstracts 83

tive as random matrices but also permit much faster signalreconstruction in one, two, and higher dimensions.

Junfeng YangNanjing Universityjfyang2992@gmail.com

Wotao YinRice Universitywotao.yin@rice.edu

Simon MorganLos Alamos National Laboratorymorga084@gmail.com

Yin ZhangRice UniversityDept of Comp and Applied Mathyzhang@rice.edu

MS45

On Globally Optimal Local Modeling: From Mov-ing Least Square to Overparametrization

This paper discusses a spectrum of methods for signal,curve, image and surface denoising, adaptive smoothingand reconstruction from noisy samples that involve lo-cally modeling the data while performing local, semi-local and/or global optimization. We show that the samemethodolgy yields many of the previously proposed algo-rithms, from the popular moving least squares methodsto the globally optimal overparametrization methods re-cently published for smoothing and optic-flow estimation.However, the unified look at the spectrum of problems andmethods also suggests a wealth of novel global functionalsand local modeling possibilities.

Alfred M. BrucksteinComputer Science DepartmentTechnion IIT, Haifa, Israelfreddy@cs.technion.ac.il

MS45

Image Super-Resolution usingSparse-Representation

Scaling up a single image while preserving is sharpnessand visual-quality is a difficult and highly ill-posed inverseproblem. A series of algorithms have been proposed overthe years for its solution, with varying degrees of success.In CVPR 2008, Yang, Wright, Huang and Ma proposeda solution to this problem based on sparse representationmodeling and dictionary learning. In this talk I presenta variant of their method with several important differ-ences. In particular, the proposed algorithm does not needa separate training phase, as the dictionaries are learneddirectly from the image to be scaled-up. Furthermore, thehigh-resolution dictionary is learned differently, by forcingits alignment with the low-resolution one. We show thebenefit these modifications bring in terms of simplicity ofthe overall algorithm, and its output quality.

Michael EladComputer Science DepartmentTechnionelad@cs.Technion.AC.IL

Matan ProtterThe CS depoartment

The Technion, Israelmatanpr@cs.technion.ac.il

Javier TurekComputer Science DepartmentTechnionjaviert@cs.technion.ac.il

Irad YavnehComputer Science Department, Technionirad@cs.technion.ac.il

MS45

Block Stein Sparse Denoising and Deconvolution

In this work, we propose fast image denoising and deconvo-lution algorithms that use adaptive block thresholding insparse representation domain. Our main theoretical resultinvestigates the minimax rates of Stein block thresholdingin any dimension d over the so-called decomposition spaces.These smoothness spaces cover the classical case of Besovspaces for which wavelets are known to provide a sparserepresentation, as well as smoothness spaces correspondingto the second generation curvelet-type construction. Weshows that block estimator can achieve the optimal mini-max rate, or is at least nearly minimax (up to a log factor)in the least favorable situation. The choice of the thresholdparameter is theoretically discussed and its optimal valueis stated for the white Gaussian noise. We provide simple,fast and easy to implement algorithms. We also report acomprehensive simulation study to support our theoreti-cal findings. The practical performance of our block Steindenoising and deconvolution algorithms compares very fa-vorably to state-of-the art algorithms on a large set of testimages.

Jalal FadiliCNRS, ENSICAEN-Univ. of Caen, FranceJalal.Fadili@greyc.ensicaen.fr

MS45

3D Sparse Representations and Inverse Problems

In this paper, we show that using a few three dimen-sional sparse transforms with atoms of different morpholo-gies, including the wavelets and two types of curvelets,we can design simple algorithms based on iterative thresh-oldings that solve many restoration and inverse problemssuch as denoising, morphological component separation,inpainting, de-interlacing or inverse Fourier/Radon trans-form with relatively few projections.

Arnaud Woiselle, Jean-Luc StarckLaboratoire AIM, CEA/DSM-CNRS-Universite ParisDiderotCEA Saclay, DAPNIA/SEDI-SAP, Serviced’Astrophysiquearnaud.woiselle@cea.fr, jstarck@cea.fr

Jalal FadiliCNRS, ENSICAEN-Univ. of Caen, FranceJalal.Fadili@greyc.ensicaen.fr

MS45

Image Modeling and Enhancement via StructuredSparse Model Selection

Joint work with Guillermo Sapiro and Stephane Mallat

84 IS10 Abstracts

An image representation framework based on structuredsparse model selection is introduced in this work. The cor-responding modeling dictionary is comprised of a family oflearned orthogonal bases. For an image patch, a model isfirst selected from this dictionary through linear approxi-mation in a best basis, and the signal estimation is thencalculated with the selected model. The model selectionleads to a guaranteed near optimal denoising estimator.The degree of freedom in the model selection is equal tothe number of the bases, typically about 10 for natural im-ages, and is significantly lower than with traditional over-complete dictionary approaches, stabilizing the representa-tion. For an image patch of size

√N × √

N , the compu-tational complexity of the proposed framework is O(N2),typically 2 to 3 orders of magnitude faster than estima-tion in an overcomplete dictionary. The orthogonal basesare adapted to the image of interest and are computedwith a simple and fast procedure. State-of-the-art resultsare shown in image denoising, deblurring, and inpainting.Demo website:http://www.cmap.polytechnique.fr/ yu/research/SSMS/demo.html

Guoshen YuECE, University of Minnesotayu@cmap.polytechnique.fr

Guillermo SapiroUniversity of MinnesotaDept Electrical & Computer Engineeringguille@umn.edu

Stephane MallatCMAP, Ecole Polytechniquemallat@cmapx.polytechnique.fr

MS46

Numerical Analysis of View Dependent Derivativesin Computed Tomography

A number of CT reconstruction formulas depend on a com-mon derivative with respect to source position. In fan-beam or helical CT, the derivative can be viewed as thedifference quotient of measurements made along parallellines and an accurate numerical implementation is crit-ical to the resolution of the reconstruction. We reviewsome of the proposed methods to implement the derivativeand present their corresponding error terms in a commonframework for fan-beam CT.

Ryan HassOregon State Universityhassr@math.oregonstate.edu

MS46

Analytic and Optimization-based Image Recon-struction in Cone-beam CT

CT hardware, algorithms, and applications have experi-enced tremendous advances in the last two decades. Inthe presentation, I will focus on discussing recently de-veloped analytic and optimization-based algorithms forimage reconstruction in cone-beam CT and their poten-tial implications for CT applications. Emphasis will beplaced on the discussion of differences between analyticand optimization-based algorithms and their implicationsfor practical applications. Examples will be used to illus-trate and clarify a number of issues, such as the relation-ship between the Nyquist sampling theorem and compres-

sive sensing approach, which seem to be confusing. Themathematic exactness of an algorithm can be an irrelevantmetric for meaningfully evaluating the algorithms practicalutility in its practical applications. Discussion will thus begiven as to how the performance evaluation of an algorithmcan be meaningfully carried out.

Xiaochuan PanThe University of ChicagoDepartment of Radiologyxpan@uchicago.edu

MS46

Band-Restricted Estimation of Noise Variance inFiltered Backprojection Reconstructions from Re-peated CT Scans

We introduce a new estimator for noise variance in tomo-graphic images reconstructed using algorithms of the fil-tered backprojection type. The new estimator operates ondata acquired from repeated scans of the object under ex-amination, is unbiased, and is shown to have significantlylower variance than the conventional unbiased estimatorfor many scenarios of practical interest. We provide an ex-tensive theoretical analysis of this estimator and presentpreliminary results with real x-ray computed tomographydata.

Adam Wunderlich, Frederic NooUtah Center for Advanced Imaging ResearchDepartment of Radiology, University of Utahawunder@ucair.med.utah.edu, noo@ucair.med.utah.edu

MS46

Motion Compensation in Computed Tomography

Clinical applications of computed tomography (CT) oftendeal with motion-contaminated data. Examples are car-diac or respiratory patient motion. We discuss motion-compensated reconstruction with 3D cone beam CT. Cur-rently there is a well-established theoretical foundation forexact 3D reconstruction of motionless phantoms, based onwork of Katsevich, Zou, Pan, Noo, Pack, Wang, Chen, andothers. However, when motion is introduced, the exactnessbreaks down. When motion is present we need to balanceexactness with stability to motion. There are known tech-niques to handle motion with approximate reconstruction,based on work of Kachelriess, Taguchi, Schechter, and oth-ers; however these approaches disregard increasing coneangle and not suitable for fully 3D reconstruction. In thistalk we propose an approach that combines elements of ex-act reconstruction with motion-gated reconstruction, andshow evaluation results.

Alexander ZamyatinToshiba Medical Researchazamyatin@tmriusa.com

MS47

From Observable Space to Parametric Space (andBack): Interpretation of earth formation struc-ture from Electro-Magnetic Measurements byAnisotropic Diffusion Maps

Given empirical data generated by a non-linear transfor-mation of some physical parameters we introduce an al-gorithm that can map newly observed data points backinto the invariant parameters space. Moreover, the algo-rithm can map a new sample from the parameters space

IS10 Abstracts 85

to the observable space. The key idea is the use of theanisotropic diffusion kernel on reference points from theobserved data to approximate a Laplacian on the inacces-sible independent parameters space. We demonstrate ourmethod in Logging While Drilling (LWD), to interpret for-mation structure from Electro-Magnetic Measurements.

Dan KushnirDepartment of MathematicsYale Universitydan.kushnir@yale.edu

MS47

Foundations of Multi-Manifold Modeling Algo-rithms

We present several methods for multi-manifold data mod-eling, i.e., modeling data by mixtures of manifolds (possi-bly intersecting). We first concentrate on the special butuseful case of hybrid linear modeling, where the underly-ing manifolds are affine or linear subspaces. We emphasizevarious theoretical results supporting the performance ofsuch algorithms as well as practical choices guided by it.This is part of joint works with E. Arias-Castro, G. Chen,A. Szlam, Y. Wang, T. Whitehouse and T. Zhang

Gilad LermanDepartment of MathematicsUniversity of Minnesotalerman@umn.edu

MS47

Multiple Scales in High-dimensional Noisy DataSets and Images

We introduce multiscale geometric methods for studyingthe geometry of noisy point clouds in high-dimensions,which may model data sets in a variety of applications.These methods allow to estimate in a robust fashion theintrinsic dimensionality of the data, to generate automat-ically dictionaries for the data, and manipulate the datafor tasks such as denoising and modeling in a way thatrespects the intrinsic geometry of the data.

Guangliang Chen, Anna Little, Mauro MaggioniDepartment of MathematicsDuke Universityglchen@math.duke.edu, avl@math.duke.edu,mauro.maggioni@duke.edu

MS47

Image De-Noising on the Manifold of Patches: ASpectral Approach

Inspired by the work of Lee and Mumford, who showedexperimentally that 3x3 patches of natural images orga-nize themselves around nonlinear low dimensional mani-folds, we propose to construct basis functions to efficientlyparametrize the manifolds of image patches. In this work,we describe how we can remove the noise from an image byiteratively reconstructing and denoising the set of patches.This approach outperforms the most successful denoisingtechniques.

Francois G. MeyerUniversity of Colorado at BoulderUSAfmeyer@colorado.edu

MS48

Reconstruction of the Orientation DistributionFunction in Q-Ball Imaging within Constant SolidAngle

Q-ball imaging is a high-angular-resolution diffusion imag-ing technique which has been proven successful in resolvingmultiple intravoxel fiber orientations. The standard com-putation of the orientation distribution function (ODF, theprobability of diffusion in a given direction) neglects thechange in the volume element along each direction. Anew technique is proposed here that, by considering thesolid angle factor, results in a dimensionless and normalizedODF expression computed from single or multiple q-shells.

Iman AganjUniversity of MinnesotaDepartment of Electrical Engineeringiman@umn.edu

Christophe LengletDepartment of Electrical and Computer EngineeringUniversity of Minnesotaclenglet@umn.edu

Guillermo SapiroUniversity of MinnesotaDept Electrical & Computer Engineeringguille@umn.edu

Essa Yacoub, Kamil Ugurbil, Noam HarelCenter for Magnetic Resonance Research, U. of Minnesotayaco0006@umn.edu, ugurb001@umn.edu,harel002@umn.edu

MS48

Diffusion Propagator Imaging: Going Beyond Sin-gle Shell HARDI

Many recent single-shell high angular resolution diffusionimaging (HARDI) reconstruction techniques have been in-troduced to reconstruct orientation distribution functions(ODF) that only capture angular information contained inthe diffusion process of water molecules. By also consider-ing the radial part of the diffusion signal, the reconstructionof the ensemble average diffusion propagator (EAP) of wa-ter molecules can provide much richer information aboutcomplex tissue microstructure than the ODF. In this talk, Iwill present recent techniques to reconstruct the EAP frommultiple shell q-space acquisitions, one of which is nameddiffusion propagator imaging (DPI). The DPI solution isanalytical and linear because it is based on a 3D spheri-cal Laplace equation modeling of the diffusion signal. Wevalidate DPI with simulations, ex vivo phantoms and alsoillustrate it on an in vivo human brain dataset. This opensperspectives in q-space acquisition schemes and lead to newways to study white matter anomalies and properties withthe diffusion propagator.

Maxime DescoteauxDepartment of Computer ScienceSherbrooke Universitym.descoteaux@usherbrooke.ca

Rachid DericheOdyssee Lab, INRIA Sophia AntipolisRachid.Deriche@sophia.inria.fr

Denis Le Bihan, J.-Francois Mangin, Cyril Poupon

86 IS10 Abstracts

NeuroSpin, CEA Saclay, Francedenis.lebihan@cea.fr, jfmangin@gmail.com,cyril.poupon@cea.fr

MS48

Recent Advances in Estimation and Processing ofHigh Angular Resolution Diffusion Images

High angular resolution diffusion imaging (HARDI) hasbecome an important magnetic resonance technique for invivo imaging. The first part of this talk focuses on estimat-ing the diffusion orientation distribution function (ODF)from raw HARDI signals. We will present an estimationmethod that naturally constrains the estimated ODF tobe a proper probability density function and regularizesthis estimate using spatial information. By making use ofthe spherical harmonic representation, we pose the ODFestimation problem as a convex optimization problem andpropose a coordinate descent method that converges to theminimizer of the proposed cost function. In the secondpart of this talk, we will present a Riemannian frameworkto carry out computations on an ODF field. The proposedframework does not require that the ODFs be representedby any fixed parameterization, such as a mixture of vonMises-Fisher distributions or a spherical harmonic expan-sion. Instead, we use a non-parametric representation ofthe ODF, and exploit the fact that under the square-rootre-parameterization, the space of ODFs forms a Rieman-nian manifold, namely the unit Hilbert sphere. Specifically,we use Riemannian operations to perform various geomet-ric data processing algorithms, such as interpolation, con-volution and linear and nonlinear filtering.

Alvina GohDepartment of Biomedical EngineeringJohns Hopkins Universityagoh@jhu.edu

MS48

Regularization of Orientation Distribution Func-tions in Diffusion MRI

Orientation Distribution Functions (ODF) are very impor-tant in Diffusion Magnetic Resonance Imaging (DiffusionMRI). They can be used as probability density functions(PDF) when applied to statistical fiber tracking of braintissues. There has been a lot of work on calculation, char-acterization and regularization of ODFs. To prepare ODFsfor fiber tracking, it is best to incorporate global informa-tion in regularization. However, since there are many vox-els involved in 3D regularization, and for each voxel thereare several directional data, which makes the global reg-ularization a 4D problem, and it is almost impossible tofinish the regularization within a bearable time. There isno fast algorithms yet published for global 3D regulariza-tion of ODFs. We will introduce a new model of globalregularization using total variation and wavelet transform.The novelty of our work is that we will implement a fastand robust method in the calculation of the global model.With the help of the fast numerical method, it is now viablefor us to work on global regularization ODF calculation,which will provide much better ODF results and improvethe accuracy of brain fiber tractography, in both single fiberdirection cases and multiple fiber direction cases.

Yuyuan OuyangDepartment of Mathematics, University of Floridaouyang@ufl.edu

Yunmei ChenDepartment of MathematicsUniversity of Floridayun@ufl.edu

Xiaojing YeDepartment of Mathematics, University of Florida358 Little Hall, Gainesville, FL32611-8105xye@ufl.edu

Ying WuRadiology Department, NorthShore UniversityHealthSystemy-wu7@northwestern.edu

MS49

Blind Motion Deblurring Using Multiple Images

We propose a novel method for automatically recovering ahigh-quality clear image from multiple blurred images. Weavoid the bottleneck of previous methods which requiredmultiple blurred image frames to be accurately aligned dur-ing pre-processing. Here instead, by exploring the sparsityof the motion blur kernel and the clear image under certaindomains, we propose an alternative approach to simultane-ously identify the blur kernels of given blurred images andrestore a clear image.

Jian-Feng CaiCAM - UCLAcai@math.ucla.edu

MS49

Flicker Stabilization in Image Sequences

Flicker is an artefact appearing in old films or in somevideos, which is characterized by intensity changes from aframe to another. Some of these contrast changes are notglobal and may be localized only on a part of the image. Inthis talk, we will introduce a new method to stabilize flickerin films. Local contrast changes are performed in order toequalize the grey level distribution of an image patch withthe grey level distributions of all its corresponding patchesin the previous and following frames. The correspondencesof a patch are computed thanks to a similarity measurethat is built to be robust to contrast changes.

Agnes DesolneuxMAP5 - Universite de Paris DescartesFranceagnes.desolneux@mi.parisdescartes.fr

Julie DelonLTCI - Telecom ParisTech - Francejulie.delon@enst.fr

MS49

Fast Dejittering for Digital Video Images Using Lo-cal Non-smooth and Non-convex Functionals

We propose several very fast algorithms to restore jittereddigital video frames (their rows are shifted) in one itera-tion. The restored row shifts minimize non-smooth andpossibly non-convex local criteria applied on the second-order differences between consecutive rows. We introducespecific error measures to assess the quality of dejittering.Our algorithms are designed for gray-value, color and noisyframes. They outperform by far the existing algorithms

IS10 Abstracts 87

both in quality and speed.

Mila NikolovaCentre de Mathematiques et de Leurs Applications(CMLA)ENS de Cachan, CNRSnikolova@cmla.ens-cachan.fr

MS49

Restoration of Home Movies

Home movies are short films, usually produced by ama-teurs, which have high cultural and historical value. Thehome movie archive of the Catholic University of Uruguayhas a large collection of movies, some in traditional filmsupport and others in Umatic tapes. We explored thespecificities of each material and the best way to restorethem while preserving its original content. In the talk wewill present the obtained results.

Alvaro PardoDIE, Universidad Catolica del Uruguayapardo@ucu.edu.uy

MS50

An Approach of Feature Detection and Fusion inFacial Recognition

Currently, most facial recognition algorithms work undercontrolled environments. In real applications, a trade-offexists between efficiency and accuracy. We proposed anapproach that performs fusion on the face area and fa-cial components (eyes, nose, and mouth). These compo-nents are also compared to the respective features of otherfaces. The proposed approach has yielded promising re-sults that demonstrate the benefits of fusion technology.High-resolution images are quickly processed to detect andrecognize slightly-angled faces accurately.

Roland ChengDefence R&D Canada Ottawar2cheng@uwaterloo.ca

MS50

Automated Sea Mine Detection, Classification, andFusion in Sonar Data

The Office of Naval Research (ONR) has sustained signif-icant research in automated sea-mine detection and clas-sification (D/C). This paper presents an overview of au-tomated D/C processing for high-resolution side-lookingsonar imagery including: normalization of sonar imagery,D/C algorithms, and Algorithm Fusion (combining mul-tiple D/C algorithms). Results from recent exercisesare given. Finally the paper presents current technicalapproaches regarding ONR’s new focus on buried-mineD/C, exploiting multi-spectral and multi-aspect data frombroadband synthetic aperture sonars.

Gerald J. DobeckNSWC PCgerald.dobeck@navy.mil

MS50

Metric Learning for Semi-supervised Clustering ofObject Representations

Practical image processing systems require matching of ob-

jects among many cameras. Once foreground subtractionhas been applied and object representations have been de-rived we perform semi-supervised clustering given a set ofpairwise constraints provided by the user aided by met-ric learning approaches. Distance metric on the manifoldof Symmetric Positive Definite matrices is represented asan L2 distance in a vector space and a Mahalanobis-typedistance metric is learnt in the new space in order to im-prove the performance of semi supervised clustering. Wewill present results in clustering people appearances fromsingle and multiple camera views.

Vassilios MorellasDepartment of Computer Science and EngineeringUniversity of Minnesotamorellas@cs.umn.edu

MS50

Adaptive Detection of Objects in Hyperdimen-sional Images via Domain-reducing Mappings

Adaptive object detectors whiten image backgrounds andthen match-filter. When the number of degrees of free-dom is large (e.g., hyperdimensional case), there may beinsufficient data for estimating background statistics. Wepresent optimal and near-optimal mappings for projectinghyperdimensional images into reduced domains and detect-ing objects of interest therein. The inverse problem: back-projecting the adaptive weights into the original domain, isalso discussed, as this is of practical importance to ill-posedproblems (e.g., tomography applications).

Firooz Sadjadi, Manuel F. Fernandez, Tom AridgidesLockheed Martin Corporationfirooz.a.sadjadi@lmco.com, manuel.f.fernandez@lmco.com,tom.aridgides@lmco.com

MS51

Global Weak Solutions for Some Nonlinear Diffu-sions

A family of nonlinear nonlocal diffusions is analyzed whichinterpolates between a Perona-Malik type equation andregular linear diffusion via the use of fractional derivatives.Solvability, global existence of strong and of a kind of weaksolutions as well as transition from non-trivial nonlinear totrivial diffusive behavior will be analyzed and numericallydemonstrated.

Patrick GuidottiUniversity of California at Irvinegpatrick@math.uci.edu

MS51

Multiphase Scale Segmentation

Variational approaches to image segmentation has beenwidely studied, specially since Mumford-Shah functionalwas proposed. Various extensions have been studied in-cluding multiphase segmentation. This talk will focus onmultiphase segmentation using size of the objects in theimage.

Sung Ha KangGeorgia Inst. of TechnologyMathematicskang@math.gatech.edu

88 IS10 Abstracts

MS51

On the Construction of Topology-preserving Defor-mation Fields

In this paper, we investigate a new method to enforce topol-ogy preservation on two-dimensional deformation fields.The method is composed of two steps: - the first one con-sists in correcting the gradient vector fields of the defor-mation at the discrete level, in order to fulfill a set of con-ditions ensuring topology preservation in the continuousdomain after bilinear interpolation. This part, althoughrelated to prior works by Karacali and Davatzikos (Es-timating Topology Preserving and Smooth DisplacementFields, B. Karacali and C. Davatzikos, IEEE Transactionson Medical Imaging, vol. 23(7), 2004), proposes a new ap-proach based on interval analysis. - the second one aimsto reconstruct the deformation, given its full set of discretegradient vector fields. The problem is phrased as a func-tional minimization problem on a convex subset K of anHilbert space V. Existence and uniqueness of the solutionof the problem are established, and the use of Lagrange’smultipliers allows to obtain the variational formulation ofthe problem on the Hilbert space V. Experimental resultsdemonstrate the efficiency of the method. Comparisonsand comments on the major differences between our modeland the one introduced by Karacali and Davatzikos are alsoprovided

Dominique AppratoUniversite de PauDept Mathematique Recherchedominique.apprato@univ-pau.fr

Christian GoutUniversite de Valenciennes, Francechris gout@cal.berkeley.edu

Carole Le GuyaderINSA Rouen, Francecarole.le-guyader@insa-rouen.fr

MS51

Global Minimization for Continuous MultiphasePartitioning Problems using a Dual Approach

This talk is devoted to the optimization problem of contin-uous multi- partitioning, or multi-labeling, which is basedon a convex relaxation of the continuous Potts model. Weprove that optimal solutions to this re- laxed problem isin fact integer valued and globally optimal to the Pott Rsmodel! In contrast to previous efforts, which are tryingto tackle the optimal labeling problem in a direct man-ner, we first propose its novel dual model and then buildup a corresponding duality-based approach. By this, theclose connections between optimal labelings and geomet-rical clustering of spatial points are revealed. In order todeal with the highly nonsmooth dual problem, we suggest asmoothing method based on the log-sum exponential func-tion and also indicate that such smoothing ap- proach for-mally gives rise to the novel smoothed primal-dual modeland suggests labelings with maximum entropy. As shownin the numerical experiments, such smoothed method forthe dual model produces an ex- pectation maximizationlike algorithm for the multi-labeling problem and yieldsbetter numerical results.

Egil BaeUniversity of Bergenegil.bae@math.uib.no

Jing YuanDepartment of Computer Science, The University ofWestern Oncn.yuanjing@googlemail.com

Xue-cheng TaiDept. of Mathematics, University of Bergen, Norway andDiv. of Math. Sciences, Nanyang Tech. Universitytai@mi.uib.no

MS52

Statistical and Computational Methods in ObjectRecognition

This course will cover existing algorithms and future chal-lenges for object recognition with a focus on statisticalmodels and computational issues. We will consider threemain tasks in the area. The first involves classificationof images containing a single object. The second involvesthe detection of objects from a particular class in largecluttered images. The third involves the challenge of label-ing multiple interacting objects in an image. We will con-sider both generative and discriminative models, emphasiz-ing their differences and similarities in terms of modeling,training and computation. Specific topics will include thenotion of invariances, low-level features, intermediate rep-resentations, learning from weakly labeled data and part-based models.

Yali AmitUniversity of ChicagoDept. of Statisticsamit@marx.uchicago.edu

Pedro FelzenszwalbUniversity of Chicagopff@cs.uchicago.edu

MS53

Frame Methodology for Dimension Reduction

Motivated by hyperspectral imaging problems, we con-struct a frame-based algorithm for dimension reductionand classification. The algorithm is formulated in termsof kernel methods, frame potential energy, and constraint-based optimal frames. The output of the algorithm is adata dependent frame. Sparse representation techniquesensure that this frame provides a frame element for eachclass to be identified to the exclusion of the other classes.The reduced dimension can be less than the number ofclasses to be analyzed.

John J. BenedettoUniversity of MarylandCollege Parkjjb@math.umd.edu

MS53

Processing and Compressing DTED and Hyper-spectral Data

We have developed new algorithms for compressing anddenoising DTED data, including multiple returns. We alsohave incorporated a new method for unmixing hyperspec-tral data using a recently developed algorithm of ArthurSzlam. We will discuss these techniques and give applica-

IS10 Abstracts 89

tions and ideas for future work.

Stanley J. OsherUniversity of CaliforniaDepartment of Mathematicssjo@math.ucla.edu

MS53

Full and Partial Pixel Methods for Spatial/spectralPattern Analysis

Automated classification methods are typically full-pixeltechniques that render hardened class labels at each sitein an image. Often the labeling is made too soon in theoverall decision process and the results are unreliable. Inthis study, a sub-pixel method constrained by full-pixelprocesses is applied to hyperspectral imagery resulting in”soft” class map layers for subsequent object recognitionand terrain analysis. The context is terrain, urban, andshallow-water mapping.

Robert RandNational Geospatial-Intelligence Agencyrobert.s.rand@nga.mil

MS53

High-Dimensional Methods Applied to Summariz-ing, Indexing, and Search Full-Motion-Video

The pace at which full motion video is being collected, frompersistent and mobile surveillance systems, is acceleratingat such a fast pace that arent enough human eyeballs tomonitor or analyze the volume of data. By taking advan-tage of a convergence of new analytics methods and ad-vanced multi/many-core computing architectures this vol-ume of video data can be reduced to a manageable set ofhigh-compressed, content-based summarization and indextables that can facilitate the searching and analysis of thedata for objects and events. This presentation describesthe use of sparse representations to build a content basedsearch engine for searching full motion EO and IR, andvideo data.

Harold E. TreasePacific Northwest National Laboratoryhet@pnl.gov

MS54

Reconstruction of Thin Tubular Objects from Elec-tromagnetic Scattering Data

We consider the inverse problem of reconstructing a collec-tion of thin tubular objects from measurements of electro-magnetic scattering data. In potential applications theseobjects could, e.g., be wires or tubes buried in the sub-surface. Applying an asymptotic representation formulafor the scattered field as the thickness of the scattererstends to zero, we establish an asymptotic characterizationof these scatterers in terms of the measurement data. Thischaracterization is then implemented in a non-iterative re-construction algorithm.

Roland GriesmaierUniversity of DelawareDepartment of Mathematical Sciencesgriesmai@math.udel.edu

MS54

Convex Source Support in Half-plane

We extend the concept of convex source support to theframework of inverse source problems for the Poisson equa-tion in an insulated half-plane. The convex source sup-port is, in essence, the smallest convex set that supportsa source that produces the measured data. We modify apreviously introduced method for reconstructing the con-vex source support in bounded domains to our unboundedsetting. The resulting algorithm is also applied to the elec-trical impedance tomography.

Lauri HarhanenAalto UniversityDepartment of Mathematics and Systems Analysisloharhan@math.tkk.fi

Nuutti HyvonenInstitute of MathematicsHelsinki University of Technolnhyvonen@math.tkk.fi

MS54

Backscattering in Electrical Impedance Tomogra-phy

Electrical impedance tomography is an imaging techniquefor recovering the admittance inside a body from boundarymeasurements of current and voltage. If the measurementprobe is small, consists of two electrodes and can be movedalong the boundary, the resulting data is of backscatter-ing nature. We note that such measurements uniquelydetermine an insulating inclusion in constant background.Moreover, we present an algorithm for reconstructing theso-called convex backscattering support of a more generalinhomogeneity.

Nuutti HyvonenHelsinki University of TechnologyInstitute of Mathematicsnuutti.hyvonen@hut.fi

Martin HankeJoh. Gutenberg-UniversitatMainz, Germanyhanke@math.uni-mainz.de

Stefanie ReusswigJohannes Gutenberg-Universitat Mainzreusswig@math.uni-mainz.de

MS54

Detecting Anomalies in Electrical Impedance To-mography

The factorization method for electrical impedance tomog-raphy (EIT) is a successful method for the detection ofanomalies, i.e. domains in which the conductivity is dif-ferent from the background conductivity. However, it isa qualitative method, i.e. it doesn’t provide the conduc-tivity inside the anomalies. We present a new version ofthe factorization method for EIT and show that it leads toa method to compute this conductivity inside previouslylocated anomalies.

Susanne SchmittUniversitat KarlsruheInstitute for Algebra and Geometry

90 IS10 Abstracts

schmitt@math.uni-karlsruhe.de

MS55

Variational Restoration of Images with Space-Variant Blur

We address the problem of space-variant image deblur-ring, where different parts of the image are blurred bydifferent blur kernels. Assuming a region-wise space vari-ant point spread function, we first solve the problem forthe case of known blur kernels and known boundaries be-tween the different blur regions in the image. We thengeneralize the method to the challenging case of unknownboundaries between the blur domains. Using variationaland level set techniques, the image is processed globally.The space-variant deconvolution process is stabilized by aunified common regularizer, thus preserving discontinuitiesbetween the differently restored image regions. We addressthe cases of space-variant out-of-focus blur, and simultane-ous motion estimation, blur segmentation and restoration.

Leah BarUniversity of Minnesotabarxx002@umn.edu

MS55

Mathematical and Computational Techniques forInverse Problems with Poisson Data

In image processing, Poisson data arises when intensitiesare measured via counting processes, e.g., when a CCDcamera is used and in positron emission tomography. Theresulting Poisson maximum likelihood reconstruction prob-lem presents both computational and mathematical chal-lenges. For one, regularization is typically needed, whichleads to theoretical questions in the realm of classical reg-ularization theory and to the problems of regularizationparameter and operator choice. Also, the resulting compu-tational problem, being large-scale and nonnegatively con-strained, is challenging and requires an efficient method. Inthis talk, we will present some results that we’ve obtainedin our effort to address these disparate challenges.

Johnathan M. BardsleyUniversity of Montanabardsleyj@mso.umt.edu

MS55

Image Restoration Using Nonlocal Mumford-ShahRegularizers

We introduce several color image restoration algorithmsbased on the Mumford-Shah model and nonlocal image in-formation. The standard Ambrosio-Tortorelli and Shahmodels are defined to work in a small local neighborhood,which are sufficient to denoise smooth regions with sharpboundaries. However, textures are not local in nature andrequire semi-local/non-local information to be denoised ef-ficiently. Inspired from recent works such as NL-means ofBuades, Coll, Morel and NL-TV of Gilboa, Osher, we ex-tend the standard models of Ambrosio-Tortorelli and Shahapproximations to Mumford-Shah functionals to work withnonlocal information, for better restoration of fine struc-tures and textures. We present several applications ofthe proposed nonlocal MS regularizers in image processingsuch as color image denoising, color image deblurring inthe presence of Gaussian or impulse noise, and color image

super-resolution. In the formulation of nonlocal variationalmodels for the image deblurring with impulse noise, we pro-pose an efficient preprocessing step for the computation ofthe weight function. In all the applications, the proposednonlocal regularizers produce superior results over the localones.

Miyoun JungDepartment of MathematicsUCLAgomtaeng@math.ucla.edu

Xavier BressonUCLADepartment of Mathematicsxbresson@math.ucla.edu

Tony ChanUniversity of California. Los Angeleschan@math.ucla.edu

Luminita A. VeseUniversity of California, Los AngelesDepartment of Mathematicslvese@math.ucla.edu

MS55

Computational Approaches for Multi-Frame BlindDeconvolution

Multi-frame deconvolution (MFBD) requires using itera-tive methods to solve large scale, nonlinear optimizationproblems. In this talk we describe an efficient variable pro-jection Gauss-Newton method to solve the MFBD prob-lem. Tikhonov regularization is incorporated using an it-erative Lanczos hybrid scheme, where regularization pa-rameters are chosen automatically using a weighted gener-alized cross validation method, thus providing a nonlinearsolver that requires very little input from the user. In ad-dition, we consider approaches that incorporate nonnega-tivity constraints and preconditioning, which provide bothadditional prior information and help to improve compu-tational efficiency.

James G. NagyEmory UniversityDepartment of Math and Computer Sciencenagy@mathcs.emory.edu

MS55

Space-Continuous Models and Algorithms for Im-age Deconvolution

To introduce to the thematic spectrum of the min-isymposium, the talk will start with an overview overminimisation-based approaches to image deconvolution.Afterwards it will focus on variational models and presentmethods to accommodate the positivity constraint withinsuch models. Firstly, this includes a reparametrisation ap-proach in connection with a gradient descent technique.Reinterpretations then lead to differential-geometric mod-els on one hand, and to interesting new fixed-point itera-tions on the other hand.

Martin WelkMathematical Image Analysis GroupSaarland Universitywelk@mia.uni-saarland.de

IS10 Abstracts 91

MS56

Discrete Optimization via Graph Cuts for NonrigidRegistration

In this presentation, we formulate non-rigid image regis-tration as a discrete labeling problem. Each pixel in thesource image is assigned a displacement label (which is avector) indicating which position in the floating image it isspatially corresponding to. A smoothness constraint basedon the first derivative is used to penalize sharp changes indisplacement labels across pixels. The whole system canbe optimized by using the graph-cuts method via alpha-expansions. We compare 2D and 3D registration results ofour method with two state-of-the-art approaches.

Albert ChungDept. of Comp. Sci. and Eng.Hong Kong Univ. of Sci. & Tech.achung@cse.ust.hk

MS56

Optimization Based Methods for Non-Rigid ImageRegistration

In my talk I will focus on numerical methods for non-rigid registration based on optimization. Starting from avariational formulation we discretize the registration prob-lem and apply efficient Newton-type optimization meth-ods such as Gauss-Newton or limited memory BFGS. Fur-thermore, I will demonstrate how to incorporate addi-tional knowledge and requirements from applications suchas landmarks or control of local volume changes by con-straint optimization.

Stefan S. HeldmannUniversity of LubeckInstitute of Mathematicsheldmann@math.uni-luebeck.de

MS56

Variational Registration with Free Form Deforma-tions

Traditionally dense deformable registration and grid based(such as free form using b-splines) deformable registrationare numerically solved using different approaches. Densedeformable registration problem is usually formulated as aniterative partial differential equation and efficiently solvedusing semi-implicit approaches. On the other hand, forfree from deformable (FFD) registration problem explicitgradient-based approaches are used. In this talk, we out-line a unified approach for solving these problems. Weshow that the grid based approaches can be interpretedas a dense deformable registration, where the interpolationkernel is built in the regularization constraint. Using thisunified approach, we gain computational efficiency whilenot compromising the quality of the match and the defor-mation field. The empirical results show the promise of theproposed approach.

Ali KhameneSiemens Corporate Researchali.khamene@siemens.com

MS56

FAIR: A Toolbox for Image Registration

Image registration is one of the challenging tasks in imageprocessing and in particular in medical imaging. Roughly

speaking, the problem is to automatically find correspon-dences between points in two different images. This talkprovides a brief introduction to image registration and out-lines a general framework, which is based on a variationalapproach. The talk also introduces the freely available soft-ware FAIR (Flexible Algorithms for Image Registration).Based on a variety of examples, it is demonstrated, whythe software is useful and how it can be used.

Jan ModersitzkiMcMaster UniversityDepartment of Computing and Softwaremodersit@cas.mcmaster.ca

MS57

Sampling Over Infinite Unions: Towards Compres-sive Ultrasonic Imaging

Real-time cardiac ultrasound suffers from complexity dueto high sampling rates. Our goal is to reduce this rate byexploiting the mathematical structure of ultrasound im-ages, captured by a union of subspaces model. We developextensions of compressed sensing (CS) to the general unionmodel including continuous-time signals by combining CSideas with traditional analog sampling theory, leading toa framework we coin Xampling (CS+sampling). We thenapply Xampling to reduce the complexity of ultrasoundimaging.

Yonina C. EldarTechnion and Stanfordyonina@ee.technion.ac.il

MS57

Sampling, Reconstruction, and Recognition of Vi-sual Signals Guided by Self-similarity

We present a non-parametric framework based on the no-tion of Kernel Regression which we generalize to adapt tolocal geometric characteristics of the given signal. Thesedescriptors are exceedingly robust in capturing the under-lying structure of multidimensional signals even in the pres-ence of significant noise, missing data, and other distur-bances. This framework is applicable to a wide variety ofproblems. Of particular interest in two and three dimen-sions are sampling and restoration. Of recent relevance tocomputer vision, are applications to object and action de-tection/recognition in images, and in video, respectively,from a single example.

Hiroyuki TakedaUC Santa Cruzhtakeda@soe.ucsc.edu

Hae Jong Seo, Peyman MilanfarEE DepartmentUniversity of California, Santa Cruzrokaf@soe.ucsc.edu, milanfar@ee.ucsc.edu

MS57

Optical Image Reconstruction from Binary Sensors

We propose an optical setup for the acquisition of imagedata using binary sensors, which is a special form of com-pressed sensing. We address the ill-posedness of the prob-lem by imposing a penalty on the total variation of thesolution. We derive the image reconstruction algorithmbased on the minimization of a corresponding convex func-

92 IS10 Abstracts

tional. We illustrate the feasibility of the approach withsome concrete examples.

Michael A. Unser, Aurelien BourquardEPFLmichael.unser@epfl.ch, aurelien.bourquard@epfl.ch

MS57

‘Rewiring’ Filterbanks for Interpolation and De-noising: Theory and Applications

This article describes a series of new results outlining equiv-alences between certain “rewirings’ of filterbank systemblock diagrams, and the corresponding actions of convolu-tion, modulation, and downsampling operators. This givesrise to a general framework of reverse-order and convo-lution subband structures in filterbank transforms, whichwe show to be well suited to the analysis of filterbank co-efficients arising from subsampled or multiplexed signals.These results thus provide a means to understand time-localized aliasing and modulation properties of such signalsand their subband representations—notions that are no-tably absent from the global viewpoint afforded by Fourieranalysis. The utility of filterbank rewirings is demon-strated by the closed-form analysis of signals subject todegradations such as missing data, spatially or temporallymultiplexed data acquisition, or signal-dependent noise,such as are often encountered in practical signal processingapplications.

Patrick J. WolfeStatistics and Information Sciences LaboratoryHarvard Universitypatrick@seas.harvard.edu

Keigo HirakawaHarvard UniversityUniversity of Daytonhirakawa@stat.harvard.edu

MS58

Differential Geometry of Curves for Large-ScaleMulti-View Stereo and Applications to BiomedicalImaging

We will present a large-scale system for automatic 3Dreconstruction of arbitrary curves and occluding surfacesfrom multiple views. The system is multi-threaded andscales up to thousands of images at high-definition, andhandles complex scenes beyond the capabilities of othermethods. The use of differential geometry for multiviewmatching and calibration are shown to be key for achiev-ing robustness. Biomedical applications which may requirefast, flexible, low-cost, and non-invasive photogrammetricsolutions will be discussed.

Ricardo FabbriBrown UniversityComputer Engineeringrfabbri@gmail.com

MS58

Comparing GPU Implementations of Bilateral andAnisotropic Diffusion Filters for 3D BiomedicalDatasets

We compare the performance of hand-tuned CUDA imple-mentations of bilateral and anisotropic diffusion filters for

denoising 3D MRI datasets. Our tests sweep comparableparameters for the two filters and measure total runtime,memory bandwidth, computational throughput, and meansquared errors relative to a noiseless reference dataset. Toassess the suitability of these implementations and param-eter choices for an image processing pipeline, we also per-form segmentation and calculate validation scores.

Mark HowisonLawrence Berkeley National Laboratorymhowison@lbl.gov

MS58

Combining Imagery, Documents, Audio, and Videoin a Multi-Domain Data Space

Technology has allowed for data collection from multi-ple domains, however the methods by which this data isscoured has not advanced in the same way. Data searchesstill rely on single-domain searches. This precludes the useof inter-domain linkages that are inherent in natural data.In this work, a set of multiple-domain subspaces are cre-ated such that a query of one type of data can directlyrecall data from all other domains

Jason KinserGeorge Mason UniversityBioinformatics and Computational Biologyjkinser@gmu.edu¿

MS58

Retinopathy Diagnosis from Ocular Fundus ImageAnalysis

Eye care can benefit from the use of ocular fundus images todiagnose pathologies. The analysis of these images requiresautomatic identification of normal and aberrant structuresin human retina such as macula, vascular network, opticdisc, hemorrhages, drusen, fovea, exudates, and microa-neurysms. Our algorithms use Hough transform to locatethe optic disk, which facilitates classification of microa-neurysms. We also consider vascular network extractionand other structures by means of mathematical morphol-ogy.

Daniela M. UshizimaVisualization and Math GroupsLawrence Berkeley National Laboratorydaniela@hpcrd.lbl.gov

Fatima MedeirosTeleinformatics Engineering DepartmentFederal University of Ceara, Brazilfsombra@ufc.br

MS59

The Unreasonable Effectiveness of Bregman Itera-tion for L1 Type Opimization

Bregman iteration was introduced to TV based restora-tion a few years ago and improved the performance signif-icantly. Later it was found that this same idea gave whatappear to be state-of-the-art fast algorithms for L1 basedoptimization problems arising in compressive sensing andelsewhere. Not only has this method been around since1967, but every new variant recently invented appears tobe closely related to and indeed often a special case ofknown techniques. So why is it a so important now? The

IS10 Abstracts 93

answer seems to be found in the nature of L1 itself. Errorscancel beautifully. I will discuss this here. This is jointwork with Wotao Yin and many other collaborators.

Stanley J. OsherUniversity of CaliforniaDepartment of Mathematicssjo@math.ucla.edu

MS59

FPC AS: A Fast Algorithm for Sparse Reconstruc-tion Based on Shrinkage and Subspace Optimiza-tion

We describe a fast algorithm for sparse reconstruction. Thealgorithm is divided into two stages that are performed re-peatedly. In the first stage, “shrinkage” yields an estimateof the subset of variables likely to be nonzero in an op-timal solution. Subspace optimization are then used torecover the magnitude of the solution in the second phase.Our implementation of this method exhibits state-of-the-art performance both in terms of its speed and its abilityto recover sparse signals.

Zaiwen WenColumbia Universityzw2109@columbia.edu

Wotao YinRice Universitywotao.yin@rice.edu

Donald GoldfarbColumbia Universitygoldfarb@columbia.edu

Yin ZhangRice UniversityDept of Comp and Applied Mathyzhang@rice.edu

MS59

A Review and Recent Results of the BregmanMethods

We review four Bregman methods that arise in applica-tions of imaging, compressed sensing, and other inverseproblems. We explain their numerical properties and high-light their relationships with the augmented Lagrangianand alternating direction methods. Recent results on the

Bregman methods are included. Applied to the �1-typeregularization, the original Bregman method has an exacterror cancellation property that leads to machine-precisionsolutions. In addition, we briefly show an exact penaltyproperty of the linearized Bregman method. These prop-erties explain the great preformance of the Bregman meth-ods. The analysis and discussions broadly apply to polyhe-dral regularization functions such the (weighted) �1-norm,anisotropic total variation, piece-wise linear functions.

Wotao YinRice Universitywotao.yin@rice.edu

MS59

An Efficient Tv-Minimization Algorithm with Ap-

plication to Single-Pixel Camera

We propose and study the use of the classic AugmentedLagrangian Method in image reconstruction in compres-sive sensing. The subproblems involved are solved througha variable splitting and alternating minimization scheme.The resulting Matlab code, called TVAL3, is comparedwith several state-of-the-art codes on both synthetic dataand real data measure by the Rice single-pixel camera.

Yin Zhang, Chengbo LiRice UniversityDept of Comp and Applied Mathyzhang@rice.edu, cl9@rice.edu

Wotao YinRice Universitywotao.yin@rice.edu

MS60

Challenges in Developing a DWI/DTI Pipeline

While diffusion MRI is already an established field, its po-tential clinical applications are still in a formative stage.One impediment to the implementation of diffusion MRIis the dearth of an established analysis framework to enableone to make valid statistical inferences and draw meaning-ful scientific conclusions, particularly from longitudinal andmulti-center data. Some unresolved issues will be describedwhose resolution would help ensure that these studies willproduce high-quality findings.

Peter J. BasserNational Institutes of Healthpjbasser@helix.nih.gov

MS60

Optimal Sampling Schemes for Diffusion MRI Ac-quisitions and Online Models Estimation

High angular resolution diffusion magnetic resonance imag-ing has been widely used in research. However, its clinicaluse remains hindered by its demand in acquisition time.New trends propose to reconstruct the diffusion model inreal-time, thus providing more flexible protocols, which canbe switched off or continued on demand. These techniquesraise new challenges, we present recent advances in mod-els estimation and acquisition design with respect to theseconsiderations.

Emmanuel CaruyerOdyssee Project TeamINRIA Sophia Antipolis-Mediterraneeemmanuel.caruyer@sophia.inria.fr

Iman AganjUniversity of MinnesotaDepartment of Electrical Engineeringiman@umn.edu

Christophe LengletDepartment of Electrical and Computer EngineeringUniversity of Minnesotaclenglet@umn.edu

Guillermo SapiroUniversity of MinnesotaDept Electrical & Computer Engineeringguille@umn.edu

94 IS10 Abstracts

Rachid DericheOdyssee Lab, INRIA Sophia AntipolisRachid.Deriche@sophia.inria.fr

MS60

A Finite Element Based Method for Quantificationof Self-diffusion Process in White Matter Environ-ment

Diffusion MRI (DMRI) is a biomedical imaging modalityfor non-invasive assessment of anatomy of white mattertracts in human brains. It offers local sensitivity of whitematter tracts to orientations of water molecules diffusivemotions. To simulate the DMRI process, we develop ahigher-order finite element method for solving the diffusionPDE in a multi-compartment environment in this work,which provides more flexibility for geometry and materialof different white tracts compartments than existing tech-niques.

Shahryar Karimi-AshtianiUniversity of Southern California, Los Angeles, CAkarimias@usc.edu

C. C. Jay KuoUniversity of Southern Califiornia, Los Angeles, CAcckuo@sipi.usc.edu

MS60

Shore in Action: Estimation of MicrostructuralFeatures from Magnetic Resonance (MR) Data

Analysis of diffusion-weighted MR data characterizes themicrostructural features of materials or tissues. The SimpleHarmonic Oscillator based Reconstruction and Estimation(SHORE) technique, which successfully represents a widerange of MR signal profiles, will be described. We will dis-cuss how the SHORE framework can be utilized to quantifyseveral characteristics of the specimen including its struc-tural anisotropy, pore size distributions, and an apparentfractal dimension.

Evren Ozarslan, Cheng Guan KoaySection on Tissue Biophysics and Biomimetics, NICHDNational Institutes of Healthozarslev@mail.nih.gov, guankoac@mail.nih.gov

Timothy M. ShepherdDepartment of Radiology & Biomedical ImagingUniversity of California, San Franciscotimothy.m.shepherd@gmail.com

NOAM Shemesh, YORAM CohenSchool of ChemistryTel Aviv University, Israelnshemesh@gmail.com, ycohen@post.tau.ac.il

Peter J. BasserNational Institutes of Healthpjbasser@helix.nih.gov

MS61

A General Framework for a Class of First OrderPrimal-Dual Algorithms for TV Minimization

We generalize the primal-dual hybrid gradient (PDHG) al-gorithm proposed by Zhu and Chan, draw connections tosimilar methods and discuss convergence of several special

cases and modifications. In particular, we point out a con-vergence result for a modified version of PDHG that hasa similarly good empirical convergence rate for total varia-tion (TV) minimization problems. Its convergence followsfrom interpreting it as an inexact Uzawa method discussed.We also prove a convergence result for PDHG applied toTV denoising with some restrictions on the PDHG step sizeparameters. It is shown how to interpret this special caseas a projected averaged gradient method applied to thedual functional. We discuss the range of parameters forwhich the inexact Uzawa method and the projected aver-aged gradient method can be shown to converge. We alsopresent some numerical comparisons of these algorithmsapplied to TV denoising, TV deblurring and constrainedl1 minimization problems.

Ernie EsserUCLA Mathematics DepartmentUniversity of California Los Angelesernmon@math.ucla.edu

Xiaoqun ZhangUniversity of California Los Angeles.xqzhang@math.ucla.edu

Tony ChanUniversity of California. Los Angeleschan@math.ucla.edu

MS61

Dynamic Network Flows and Nonlinear DiscreteTotal Variation Evolutions

We consider combinatorial minimization algorithms forsolving some variational image processing problems. Inparticular, we consider energies involving Discrete TotalVariations. Their minimizations yield a differential inclu-sion problem that can be efficiently solved via parametricmaximum-flow. A maximum-principle follows. Links withfirst-order methods, Hamilton-Jacobi equations and con-servations are described.

Jerome DarbonUCLAjerome@math.ucla.edu

MS61

Non-local Regularization of Inverse Problems

This article proposes a new framework to regularize lin-ear inverse problems using a total variation prior on anadapted non-local graph. The non-local graph is optimizedto match the structures of the image to recover. This allowsa better reconstruction of geometric edges and texturespresent in natural images. A fast algorithm computes iter-atively both the solution of the regularization process andthe non-local graph adapted to this solution. The graphadaptation is particularly efficient to solve inverse problemswith randomized measurements such as inpainting randompixels or compressive sensing recovery. Our non-local reg-ularization gives state of the art results for this class ofinverse problems. On more challenging problems such asimage super-resolution, our method gives results compara-ble to translation invariant wavelet-based methods.

Gabriel PeyreCeremade, Universite Paris Dauphinegabriel.peyre@ceremade.dauphine.fr

IS10 Abstracts 95

Sebastien BougleuxUniversity of CaenGREYC CNRSsebastien.bougleux@unicaen.fr

Laurent D. CohenCNRS, UMR 7534Universite Paris-Dauphine, CEREMADEcohen@ceremade.dauphine.fr

MS61

Image Restoration by Tikhonov RegularizationBased on Generalized Krylov Subspace Methods

We describe Tikhonov regularization of large linear dis-crete ill-posed problems with a regularization operator ofgeneral form and present an iterative scheme based on ageneralized Krylov subspace method. This method simul-taneously reduces both the matrix of the linear discreteill-posed problem and the regularization operator. The re-duced problem so obtained may be solved, e.g., with theaid of the singular value decomposition. Also, multipa-rameter Tikhonov regularization is discussed. Numericalresults illustrate the promise of problem-oriented operatorin image denoising and deblurring.

Fiorella SgallariUniversity of BolognaDepartment of Mathematics-CIRAMsgallari@dm.unibo.it

Reichel LotharDepartment of Mathematical Sciences, Kent StateUniversityreichel@math.kent.edu

Qiang YeDept of MathUniv of Kentuckyqye@ms.uky.edu

MS62

Multiscale Geometry and Probability Measures onPlane Curves

We will construct some families of probability measures onequivalence classes of plane curves, where the equivalencerelations depend on the local regularity of the curve atdifferent scales. We will also discuss sampling from thesedistributions.

Matt FeiszliYale, Mathematicsmatt.feiszli@yale.edu

MS62

Spectral Gromov-Wasserstein Distances for ShapeMatching and the Role of Scale

We introduce a spectral notion of distance between shapes(closed Riemannian manifolds) and study its theoreticalproperties. We show that our distance satisfies the prop-erties of a metric on the collection of isometry classesof Riemannian manifolds. Our construction is similar tothe Gromov-Wasserstein distance, but rather than view-ing shapes as metric spaces, we define our distance viathe comparison of heat kernels. This is possible since theheat kernel characterizes the shape up to isometry. By

establishing two different hierarchies of lower bounds, werelate our distance to previously proposed spectral invari-ants used for shape comparison, such as the spectrum ofthe Laplace-Beltrami operator and statistics of pair-wisediffusion distances. Lower bounds in these hierarchies pro-vide increasing discriminative power at the expense of moreinvolved computations.

Facundo MemoliStanford University, Mathematics Departmentmemoli@math.stanford.edu

MS62

On the Localization Behavior of Graph LaplacianEigenfunctions Over Dendrite Structures

We report our observation and analysis of the eigenvaluedistribution of the Laplacian of graphs representing neu-ronal dendrite patterns, and the behavior of the corre-sponding eigenfunctions. In particular, we discuss a “phasetransition’ phenomenon occurring at the eigenvalue 4. Theeigenfunctions corresponding to the eigenvalues below 4 aresemi-global oscillations (like Fourier modes) over the den-drite arbors whereas those corresponding to the eigenvaluesabove 4 are localized (like wavelets) in branching regions.

Naoki Saito, Ernest WoeiDepartment of MathematicsUniversity of California, Davissaito@math.ucdavis.edu, woei@math.ucdavis.edu

MS62

The Multiscale Flat Norm for Shape Signatures

In this talk, I will discuss the application of the New Mul-tiscale Flat Norm to shapes. Computations are carriedout using graph cut methods with 16 neighbors. As a re-sult the minimizers computed are actually minimizers ofan anisotropic energy that approximates the usual TV en-ergy. Some details, involving a simple but cumbersomeleast squares calculation, yields slightly better weights thanthose which are obtained through the usual Crofton’s For-mula method.

Kevin R. Vixie, Keith ClawsonWashington State Universityvixie@speakeasy.net, rattletyboom@gmail.com

Brandon PriceWalla Walla Universitybrandon.price@wallawalla.edu

Gary SandineLos Alamos National Laboratorygars@lanl.gov

Thomas J. AsakiWashington State Universitytasaki@wsu.edu

MS63

Numerical Methods for Optimal Mass Transportwith Applications to Image Registration

Optimal mass transport refers to an optimization problemin which mass is optimally transported. In recent work,Benmou and Brenier have shown that although the orig-inal formulation is highly nonlinear and non-convex it is

96 IS10 Abstracts

possible to reformulate the problem as a convex, PDE con-strained optimization problem. In this talk we considerefficient numerical techniques for the solution of the re-sulting problem. We show that the formulation leads toa problem a-kin to nonlinear flow in porous media. Wethen discuss discretization and effective multigrid solutionto the problem

Eldad HaberDepartment of MathematicsThe University of British Columbiahaber@math.ubc.ca

Raya HoreshEmory UniversityAtlanta, GArshindm@emory.edu

MS63

Gauss-Newton Optimization in the Large Deforma-tion Diffeomorphic Metric Mapping

The Large Deformation Diffeomorphic Metric Mapping(LDDMM) can be considered among the pioneeringparadigms for diffeomorphic registration in ComputationalAnatomy. Although LDDMM is embedded into a rigorousmathematical framework where anatomical variability canbe properly studied, the huge computational complexityinherent to the use of the non-stationary parameterizationof diffeomorphisms constitutes its important practical lim-itation. In order to alleviate the computational require-ments of LDDMM, different variations focused on diffeo-morphism characterization have been proposed in the liter-ature. Much less attention has been paid to the optimiza-tion strategy in LDDMM, where classical gradient descentis often used. As shown in alternative non-rigid registra-tion paradigms, the use of efficient second-order optimiza-tion techniques may improve the rate of convergence duringoptimization thus reducing time requirements in LDDMMwith an affordable increase of the needed memory per itera-tion. In this talk, I will present a numerical implementationof Gauss-Newton’s method for second-order optimizationin LDDMM for both non-stationary and stationary param-eterizations. The computations of the Gateaux derivativesof the corresponding objective functions are performed inthe tangent bundle of the Riemannian manifold of diffeo-morphisms. Two different approaches for the computa-tion of the Gateaux derivatives associated to the station-ary parameterization of diffeomorphisms lead to two dif-ferent algorithms for Gauss-Newton stationary LDDMM.The three proposed Gauss-Newton LDDMM methods havebeen compared to their respective versions of gradient de-scent LDDMM using the non-rigid registration evaluationproject (NIREP) databases. I will report the advantages ofGauss-Newton with respect to gradient descent optimiza-tion for the three methods. Finally, I will also show theadvantages of performing optimization in the tangent bun-dle with respect to optimization in the space of squaredintegrable functions proposed in Dartel.

Monica HernandezUniversity of Zaragoza, Spainmhg@unizar.es

MS63

Diffeomorphic Demons for Image Registration

In this talk, we will present the evolution of the demons’algorithm over a decade. Originally proposed by Thirion

as an efficient procedure for non-linear registration, the al-gorithm was revisited several times to be recast in a soundminimization framework, in particular through Cachier’spair and smooth (PASHA) method. Additional modifica-tions were performed bu Stefanescu to make it fully par-allelizable and to include a non-stationnary adaptive reg-ularization that could take into account pathologies (areasthat do no correspond). Recently, Vercauteren adaptedthe efficient optimization procedure to work on a space ofdiffeomorphic transformations, which leads to the diffeo-morphic demons. Our experiments show that the resultsare similar in terms of image similarity metric, but moreregular and closer to the true transformation in controlledexperiments, particularly in terms of Jacobian. Follow-ing the proposition of Arsigny to parameterize (some of)the diffeomorphism using one parameter subgroups, we willfinally present the symmetric version and the statisticalframework on diffeomorphisms that we could build on itresults.

Xavier PennecINRIA Sophia-Antipoolis Meditrerraneexavier.pennec@sophia.inria.fr

MS63

Unbiased Nonlinear Image Registration

We present a novel unbiased nonlinear image registrationtechnique. The unbiased framework generates theoreticallyand intuitively correct deformation maps, and is compati-ble with large-deformation models. We apply informationtheory to quantify the magnitude of deformations and ex-amine the statistical distributions of Jacobian maps in thelogarithmic space.

Igor YanovskyJet Propulsion Laboratory, California Institute ofTechnologigor.yanovsky@jpl.nasa.gov

Alex LeowUniversity of Illinois, Chicagoalexfeuillet@gmail.com

Stanley J. OsherUniversity of CaliforniaDepartment of Mathematicssjo@math.ucla.edu

Paul M. ThompsonDepartment of NeurologyUCLA School of Medicinethompson@loni.ucla.edu

MS64

SD-OCT Image Segmentation in Retinal PathologyAssessed with Adaptive Optics

Our lab uses adaptive optics ophthalmoscopy to image thecone mosaic in a variety of retinal pathology. Adaptive op-tics enables visualization of individual cone photoreceptors,so we can quantify the degree of degeneration. SD-OCT isa more prevalent imaging technology, and here we presentdata on extracting information from SD-OCT images inthese clinical cases. Common metrics like layer thicknesscan be insensitive to dramatic cone disruption, so alterna-tive image analysis tools are needed.

Joseph Carroll

IS10 Abstracts 97

Medical College of Wisconsinjcarroll@mcw.edu

Hitesh TannaMarquette University@marquette.edu

Diane M. Tait, Jungtae Rha, Pooja Godara, Kimberly E.StepienMedical College of Wisconsin@mcw.edu, @mcw.edu, @mcw.edu, kstepien@mcw.edu

MS64

Introduction to SDOCT imaging and RegisterationUsing Generalized Pseudo-Polar Fourier Grids

Fast and accurate estimation of the Fourier transform inpolar coordinates has long been a major challenge for manyimage processing applications. To address this problem, ithas been proposed to calculate the Fourier transform co-efficients on the pseudo-polar coordinates. To acquire bet-ter image registration accuracy, we introduce the general-ized pseudo-polar motion estimation framework that en-compasses the classic pseudo-polar and related techniques.Experimental results on neonatal SDOCT images attest tothe effectiveness of this method.

Sina Farsiu, Nigel Chou, Cynthia A. Toth, Joseph A. IzattDuke Universitysina.farsiu@duke.edu, nigel.chou@gmail.com,cynthia.toth@duke.edu, jizatt@duke.edu

MS64

Imaging Processing Techniques for Adaptive Op-tics Fourier Domain Optical Coherence Tomogra-phy

Adaptive optics Fourier domain optical coherence tomog-raphy (AO-FDOCT) is a relatively new retinal imagingtechnique that provides micron-level axial and lateral reso-lution in the live eye by dynamic correction of ocular aber-rations. AO-FDOCT systems contain at least two imagersand require several parallel stages of real-time processingand control for efficient feature extraction, visualization,and manipulation. Post-processing algorithms, for exam-ple those for segmentation, registration, and Doppler phaseretrieval, are used to enhance and discriminate signal fromnoise or to delineate tissue margins. Both established andnew techniques will be discussed.

Daniel X. Hammer, Mircea Mujat, Nicusor V. Iftimia,Nuyom Lue, R. Daniel FergusonPhysical Sciences Inc.hammer@psicorp.com, mu-jat@psicorp.com, iftimia@psicorp.com, lue@psicorp.com,ferguson@psicorp.com

MS64

Applications of Adaptive Optics - Ultra-high Reso-lution Optical Coherence Tomography for In VivoRetinal Imaging and Visualization

Recent developments in adaptive optics - optical coher-ence tomography (AO-OCT) allow for real time ultra-highisotropic resolution imaging of the in-vivo retina, offeringunprecedented insight into its volumetric microscopic andcellular structures. To achieve full potential of this tech-nique for clinical ophthalmic applications novel image ac-

quisition and visualization methods as well as data pro-cessing techniques has to be implemented. We will describeour AO-UHR-OCT system and techniques developed in ourlaboratory that allow its use for in-vivo clinical imaging.

Robert J. ZawadzkiUniversity of California Davisrjzawadzki@ucdavis.edu

Steven M. JonesLawrence Livermore National Laboratory@llnl.gov

Suman PilliUniversity of California Davissuman.pilli@ucdmc.ucdavis.edu

Scot S. OlivierLawrence Livermore National Laboratoryolivier1@llnl.gov

John S. WernerUniversity of California Davisjswerner@ucdavis.edu

MS65

The Role of Similarity Measures in Face Recogni-tion

A fundamental challenge in face recognition lies in deter-mining which steps are important in the recognition offaces. Several studies have indicated the significance ofcertain steps in this regard, particularly preprocessing andfeature extraction. Surprisingly, however, it has not beenmade clear whether the similarity measures play an im-portant role in the recognition of faces. Here, we reportexperimental results which suggest that for face recogni-tion the similarity measures are influential.

Arjun V. Mane

Dr. B A Marathwada University, Aurangabad (MS) Indiaarjunmane7113@yahoo.co.in

Ramesh Manza, Karbhari KaleDr. B A M University, Aurangabadramesh manza@yahoo.com, kvkale91@gmail.com

MS65

Person Detection and Tracking for Large-scaleSurveillance

Person detection and tracking for large sites is challengingdue to a variety of reasons. The scenes can get crowded,and in such instances crowd segmentation techniques areneeded to separate individuals. The large areas to be cov-ered may require several non-overlapping cameras, andtracking between them requires person re-identification.For city-wide surveillance, cameras mounted on mobileplatforms may be required. This talk is concerned withresearch that has been done in the areas of multi-cameraperson detection and tracking, crowd segmentation, personreidentification, and person detection for moving cameras.

Thomas B. SebastianGE Global Researchsebastia@ge.com

98 IS10 Abstracts

MS65

Understanding Crowded Visual Scenes

Most video surveillance/monitoring approaches assume thecapability to reliably track individuals, thus failing incrowded environments where such tracking is difficult. Wefirst model dense crowd scenes using Lagrangian particledynamics to segment crowd flows and detect flow instabil-ities. Then, observing that pedestrian behavior in crowdsresults from collective behavioral patterns evolving fromlarge numbers of individuals interacting among themselvesand the scene geometry, we generate an algorithm for track-ing an individual within the crowd.

Mubarak ShahUniversity of Central Floridashah@cs.ucf.edu

MS65

Dimensionality Reduction and Sparsity for ObjectRecognition

A large body of work has been performed recently explor-ing ideas in dimensionality reduction, sparse representa-tions and compressed sensing. Some work has begun tomerge machine learning and dimensionality reduction andsparsity, utilizing these ideas to improve image recognitionperformance. This talk will focus on usage and perfor-mance of geometric diffusion and sparse representations forpattern recognition in challenging imaging conditions.

Alan Van NevelImage and Signal Processing Branch, ResearchDepartmentNAWC, Weapons Divisionalan.vannevel@navy.mil

PP0

Use of Machine Vision for Online Estimation ofCoal Fines on Conveyor Belts

Excessive fines in coal fed to power stations, metallurgi-cal furnaces and other fixed or fluidized bed reactors cancause major problems by adversely affecting the flow of gasthrough the solid burden. In this industrial case study, thenovel application of machine vision to monitor coal on con-veyor feed systems is described. By making use of a mod-ified adaptive thresholding algorithm, the fines content inthe stratified coal could be estimated reliably.

Chris AldrichDepartment of Process EngineeringUniversity od Stellenboschca1@sun.ac.za

PP0

A Modified Piecewise Constant Mumford-ShahModel Based Simultaneous Segmentation and Reg-istration

A new variational region based model for a simultaneousimage segmentation and registration is proposed. The seg-mentation is obtained by minimizing a modified piecewiseconstant Mumford-Shah model and registration is assistedby the segmentation information and region intensity val-ues. The numerical experiments of the proposed model aretested against synthetic data and simulated normal noisyhuman-brain magnetic resonance (MR) images. The pre-liminary experimental results show the effectiveness of the

proposed model.

Jung-Ha AnMathematics DepartmentCalifornia State University, Stanislausjan@csustan.edu

Yunmei ChenUniversity of Floridayun@math.ufl.edu

PP0

Image Diffusion and Sharpening Via High-OrderSobolev Gradient Flows

We utilize Sobolev gradients for image diffusion and sharp-ening and show that reformulating the gradient flow forthe heat equation energy functional under various Sobolevmetrics yields well posed flows both forward and backward.This opens the door to applications such as image sharp-ening via reverse diffusion. We present several theoreticalresults in this direction as well as favourable comparisonsto the Shock Filter with striking further improvements asthe Sobolev order is increased.

Jeff Calder, Abdol-Reza MansouriDepartment of Mathematics and StatisticsQueen’s Universityjcalder@mast.queensu.ca, mansouri@mast.queensu.ca

Anthony YezziSchool of Electrical and Computer EngineeringGeorgia Institute of Technologyanthony.yezzi@ece.gatech.edu

PP0

Improving Small Angle X-Ray Scattering for Mod-ern Computing

Small angle X-ray scattering (SAXS) is a technique tofind the structure of biological macromolecules. Imagingmacromolecules via SAXS is an inverse problem. The dif-ficulty is that the inverse problem associated with SAXS isill-posed and ill-conditioned. Traditionally, many physicalsimplifications are made to work around this. The CSUSAXS group is proposing to strengthen SAXS with a newmodeling approach and new computationl methods that donot impose these simplifications.

Ryan CrokeColorado State Universityrpcroke@gmail.com

PP0

3D Tensor Factorization for Video Restoration

We have applied blind source separation (BSS) techniques,such as independent component analysis and dependentcomponent analysis, to video restoration, where the com-monly used point spread function (PSF) information inblind or non-blind deconvolution is not required. However,these matrix factorization based BSS methods have limi-tations. For instance, image local spatial structure is notused, and constraints should be imposed for unique solu-tions. In this paper, we will investigate 3D tensor factor-ization for video restoration. It is expected that the qualityof the restored image will be improved with simpler imple-mentation due to its model-free and constraint-free nature.

IS10 Abstracts 99

The restored image can be further enhanced by formulat-ing a second multi-channel image restoration problem viaGabor filtering, where 3D tensor factorization is appliedagain to achieve final enhancement.

Qian DuMississippi State Universitydu@ece.msstate.edu

Ivica KoprivaRudjer Bokovic Institute, Zagreb, Croatiaikopriva@gmail.com

PP0

Synthetic Boundary Conditions and Precondition-ing for Image Deblurring Problems

Given a blurred image and the corresponding blurring op-erator, we try to restore the original unblurred image. Wedo not use the classical periodic or Neumann boundaryconditions. The boundary conditions we use are directlyderived from the blurred images and we name it syntheticboundary conditions. The resulting deblurred images arebetter than those under classical assumptions. We havealso developed an effective regularized DCT preconditionerto solve these difficult large-scale imaging problems.

Ying Wai FanEmory Universityyfan@emory.edu

James G. NagyEmory UniversityDepartment of Math and Computer Sciencenagy@mathcs.emory.edu

PP0

A Piecewise Smooth Region Based SimultaneousImage Segmentation and Non-Rigid Registration

The goal of the paper is to segment and register novelimages simultaneously using a modified piecewise smoothMumford-Shah technique and region intensity values. Thesegmentation is obtained by minimizing a modified piece-wise smooth Mumford-Shah model. A non-rigid registra-tion is assisted by the segmentation information and regionintensity values. The numerical experiments against syn-thetic data and simulated normal noisy human-brain mag-netic resonance (MR) images show the effectiveness of thepresented model.

Jung-Ha AnMathematics DepartmentCalifornia State University, Stanislausjan@csustan.edu

Michael FosterCalifornia State University Stanislausfostermc416@msn.com

PP0

Inverse Illumination Techniques for Automated Vi-sual Inspection

Many industrial inspection tasks can be accomplished bycomparing a test object with a master object. We reviewillumination techniques that aim to minimize the effort ofdefect detection by encoding knowledge about the mas-

ter object into the process of image formation. Basedon this idea we propose an illumination technique using aprojector-camera system that directly displays differencesbetween the two objects by projecting an inverse illumina-tion mask of the master object.

Robin GrunaKarlsruhe Institute of TechnologyLehrstuhl fur Interaktive Echtzeitsystemerobin.gruna@kit.edu

Jurgen BeyererFraunhofer-Institut fur Informations- undDatenverarbeitungjuergen.beyerer@iitb.fraunhofer.de

PP0

Shapes from Geometric Measures

In this work we show that shapes can be reconstructedfrom simple non asymptotic densities measured only alongedge shapes. The particular density we study correspondsto the area of a disk centered on the boundary that is alsoinside the shape. It is easy to show uniqueness when thesedensities are known for all radii in a neighborhood of r =0, but much less straightforward when we assume we knowit for (almost) only one r ¿ 0. We present variations ofuniqueness results for polygons and smooth curves undercertain regularity conditions.

Sharif Ibrahim, Kevin R. VixieWashington State Universitysibrahim@math.wsu.edu, vixie@speakeasy.net

Kevin SonnanburgWhitworth Universityksonnanburg10@whitworth.edu

PP0

A Fully Automated Approach to Segmentation andRegistration of Medical Image Data for PulmonaryDiagnosis

Molecular imaging is an important tool in drug devel-opment but generates large amounts of data, demand-ing for fully automated analysis tools. We propose anovel fully-automated approach to the analysis of venti-lation/perfusion SPECT data acquired in the context ofpulmonary diseases. Particularly, we propose a modifica-tion of the Chan-Vese approach for a stable segmentationwhich then serves as a starting point in a spatial alignmentprocess. Our results demonstrate the potential of the newapproach.

Alvin I. IhsaniMcMaster UniversityComputing and Softwareaihsani@gmail.com

Jan ModersitzkiMcMaster UniversityDepartment of Computing and Softwaremodersit@cas.mcmaster.ca

Troy FarncombeMcMaster UniversityRadiologyfarncomb@hhsc.ca

100 IS10 Abstracts

PP0

Texture - Noise Separation

It is a very ill-posed problem to recover a clean image froma noisy blurred image simply because deblurring and de-noising processes are contradicting in that deblurring issharpening process and denoising is smoothing process. Inthis model, we collect some a priori information about purenoise and pure texture by using different Sobolev spaces ofnegative differentiability, which will provide noticeably dif-ferent behaviors, and incorporate them to distinguish noisefrom texture.

Yunho KimDepartment of MathematicsUniversity of California, Irvineyuno1123@math.uci.edu

PP0

A Variational Joint Framework for Deblurring, De-noising and Segmenting.

In this talk, we propose a variational joint framework forboth restoration (deblurring and denoising) and segmenta-tion of blurred and noisy images. We aim to solve, by an al-ternating framework, an extended modified Mumford-Shahfunctional. The segmentation stage based on the ActiveContours Without Edges and solved using Sobolev Gra-dients and Additive Operator Splitting schemes, allows topartition the image domain into several subdomains. Thesesubdomains are then used to parallelize the computationsof the discretized PDE related to the restoration stage.Details of the numerical analysis as well as numerical ex-periments are provided.

Carole Le GuyaderINSA Rouen, Francecarole.le-guyader@insa-rouen.fr

Christian GoutUniversite de Valencienneset du Hainaut-Cambresischristian.gout@univ-valenciennes.fr

Isabelle RamiereCEA, Franceisabelle.ramiere@cea.fr

PP0

Direct Sparse Deblurring

We propose a deblurring algorithm that explicitly takesinto account the sparse characteristics of natural imagesand does not entail solving a numerically ill-conditionedbackward-diffusion. The key observation is that the sparsecoefficients that encode a given image with respect to anover-complete basis are the same that encode a blurred ver-sion of the image with respect to a modified basis. Follow-ing an “analysis-by-synthesis’ approach, an explicit gener-ative model is used to compute a sparse representation ofthe blurred image, and the coefficients of which are used tocombine elements of the original basis to yield a restoredimage. We compare our algorithm against the state of theart in deblurring algorithms.

Yifei LouUniversity of California Los Angelesyflou@math.ucla.edu

PP0

Comparing Regularized Cut to Normalized Cut

In comparing two segmentation algorithms approximatingthe Normalized Cut criterion, both returned reasonablesegmentations for images with simple backgrounds. Thetwo algorithms we considered are Hochbaums NormalizedCut approximation, which we have called Regularized Cut,and Shi and Maliks Normalized Cut algorithm. Regular-ized Cut can have more flexibility, since it requires someuser interaction, and in practice, Regularized Cut runsfaster than Normalized Cut.

William S. MonroeUniversity of Iowawmonroe@engineering.uiowa.edu

Xiaodong WuElectrical and Computer Engineering DepartmentUniversity of Iowaxiaodong-wu@uiowa.edu

Yusung KimRadiation Oncology DepartmentUniversity of Iowayusung-kim@uiowa.edu

PP0

A Mechanical Bidomain Model of the Heart

When representing the electrical properties of the heartwith the bidomain model, one distinguishes between theintracellular and extracellular spaces. We develop a bido-main model for the mechanical properties of the heart,accounting for the different mechanical properties insideand outside the cells. This is particularly relevant in caseswhere the intracellular and extracellular (e.g. Lorentz)forces are in opposition. Uses include analysis of displace-ment of current carrying tissue in MRI.

Steffan M. Puwal, Bradley RothDepartment of PhysicsOakland Universitysmpuwal2@oakland.edu, roth@oakland.edu

PP0

Measuring Conductivity of Biological Tissue UsingMagnetic Induction Tomography

Magnetic Induction Tomography is finding use as an ex-perimental tool for mapping the conductivity of biologicaltissues. Our numerical approach is to obtain a Fourier ex-pansion of the relevant stream functions relating the mag-netic fields, eddy current density, and conductivity (resis-tivity). Thus, we are able to add noise to the system anddetermine the fidelity of the measured signal to the trueconductivity map. We focus on representations of cardiactissue.

Steffan M. Puwal, Bradley RothDepartment of PhysicsOakland Universitysmpuwal2@oakland.edu, roth@oakland.edu

PP0

Efficient Implicit Smooothing of Contour Lines for

IS10 Abstracts 101

Image Reconstruction

The standard approach to image reconstruction typicallyproduces noisy object boundaries. By contrast to explicitedge-field models, we propose to incorporate the smooth-ness of the contour lines in an implicit way by introducingan additional penalty term defined in the wavelet domain.We also derive an efficient stress-majorization algorithmto solve the associated optimization problem. Our tech-nique produces visually pleasing reconstructions which arequantitatively better than those obtained without waveletdomain constraints.

Marc C. RobiniCREATISINSA Lyonmarc.robini@creatis.insa-lyon.fr

Jean-Philippe LabruyereDePaul Universityjpl@cs.depaul.edu

PP0

A Basis Pursuit Approach for Multi-Scale Am-FmReconstructions

Recently a new multi-scale amplitude-modulationfrequency-modulation (AM-FM) demodulation method forimage processing was introduced. The model function con-siders the sum of the product of the instantaneous ampli-tude (IA) times the cosine of L harmonics of the instanta-neous phase (IP) as the independent variables. We proposeto consider the L harmonics of the IP as the basis of anovercomplete dictionary within the Basis Pursuit frame-work.

Paul RodriguezPontifical Catholic University of Peruprodrig@pucp.edu.pe

Victor Murray, Marios PattichisUniversity of New Mexicovmurray@ieee.org, pattichis@ece.unm.edu

PP0

Denoising Using Decomposition

In an earlier work, the author proposed a new decorre-lation term to be added to the decomposition model ofOsher, Sole and Vese, with favourable results obtained. Inthe present work, the new term is used for the purpose ofdenoising textured images. Time permitting, other new ex-tensions to decomposition models will also be discussed fortexture denoising. Finally, some applications to real-worldimaging will be shown.

Reza ShahidiMemorial University of Newfoundlandreza.shahidi@gmail.com

PP0

Data Fusion of Combined High Spatial ResolutionX-Ray CT and High Temporal Resolution Electri-cal Impedance Tomography Imaging

CBCT is a high spatial resolution imaging system. It suf-fers from low temporal resolution and consequently frommotion artefacts. EIT can generate images with high tem-

poral resolution and poor spatial resolution. An EIT-CBCT modality has been investigated in this study. Mo-tion information was extracted from EIT images. The mo-tion data then has been implemented into CBCT recon-struction for compensating the motion. CT images withreduced motion artefacts could be observed by this dualmodality.

Thanyawee PengpanDepartment of Electronic and Electrical Engineering,University of Bathtp257@bath.ac.uk

Cathryn Mitchell, Manuchehr SoleimaniDepartment of Electronic and Electrical EngineeringUniversity of Bathc.n.mitchell@bath.ac.uk, m.soleimani@bath.ac.uk

PP0

Spatio-Spectral Anomalous Change Detection inHyperspectral Imagery

Given two images of the same scene, taken at differenttimes and under different conditions, the aim of anomalouschange detection is to distinguish the pervasive differences(due for instance to illumination or calibration effects) fromthe actual changes that have occurred in the scene. Thisposter will present an approach for combining local spatialcontext with the spectral properties of a pixel for the pur-pose of identifying anomalous changes in pairs of images.

James TheilerSpace and Remote Sensing SciencesLos Alamos National Laboratoryjt@lanl.gov

PP0

Graph Based DenoisingUsing Local Non-Parametric Image Graph Modi-fications: Variations and Applications

In this work, we describe experiments that explore the re-cent image denoising and segmentation methods of Asakiet al. in which minor modifications to the now classical lo-cal numerical methods produce good results in cases of lowto medium noise. These modifications are based on con-structions of subgraphs of the standard nearest-neighborgraph commonly used in numerical computations of gra-dients. We investigate the precise ways in which the newmethods succeed and fail, explaining what we mean by suc-cess and failure. The central feature of the innovation isthe non-parametric nature of the graph modifications.

Thomas Asaki, Keith Clawson, Benjamin Van Dyke,Heather Van DykeWashington State Universitytasaki@wsu.edu, kclawson@wsu.edu,bennyvandyke@yahoo.com, vandykeheather@yahoo.com

PP0

Convolution Equations and Digitization

The main goal of this paper is approximation of convo-lution equation on a straight line by a system of linearalgebraic equations in a following way. First given convo-lution kernel one writes out discrete convolution kernel bydirect digitization of continuous kernel, and then the dis-

102 IS10 Abstracts

crete kernel will be cut off and periodically extended on awhole discrete line (so called cyclic convolution). It per-mits to solve the finite system of linear algebraic equationsby using fast Fourier transform.

Vladimir B. VasilyevDepartment of Mathematics and InformationTechnologiesBryansk State Universityvbv57@inbox.ru

Alexander VasilyevDepartment of Physics and MathematicsBryansk State Universityalexvassel@gmail.com

PP0

Small Sample Histograms Variabilty

Small sample histograms have extreme variabilty as doessmall-sample-just-about-everything. However for uniformbin width histograms, extreme shape variability challengestheir usefulness. Shape variability can be understood andcontrolled by first obtaining all possible shapes via par-titioning the space of bin locations and width into shapelevel sets. The level sets allow method of moments andmaximum likelihood procedures to be used to obtain rep-resentative small sample histograms. This builds on J. R.Thompson’s 1978/1990 histogram maximum likelihood re-sult.

James S. WeberOR and Statistics ConsultantJamesSWeber@gmail.com

PP0

Variational Model for Depth from Motion Blur

A variational method for combined deblurring and depthestimation from a single still image degraded by spatiallyvariant motion blur is presented. The blur is assumed tobe caused by translatory camera motion. The variationalmethod is based on minimising an energy functional withrespect to the sharpened image and depth field simultane-ously. Experiments on synthetic data confirm the viabilityof the approach.

Steffen LoeschUniversity of Cambridgeloeschsteffen@googlemail.com

Martin WelkMathematical Image Analysis GroupSaarland Universitywelk@mia.uni-saarland.de

PP0

Block Estimation Methods in Exemplar-Based Im-age Restoration

Exemplar-based methods have recently been shown to givecompetitive performance in a variety of image restora-tion tasks, including denoising, inpainting, and super-resolution. One of the most important aspects of anexemplar-based method is the actual block estimation, forwhich a rather diverse range of algorithms has been ap-plied. We present the results of an extensive set of ex-periments comparing a number of the leading algorithms

within a common context.

Brendt WohlbergLos Alamos National Laboratorybrendt@lanl.gov

PP0

Hermite Polynomials in a Searching for GlobalMaximum Position

Analysis of multiextreme functions for maximum is basedon the Hermite polynomials series of function symmetrizedaround objective (anknown) point. This method searchesfor a global maximum position and in recursive iterationsallows to find all significant maxima.

Yuriy A. YatsunenkoFermi National Accelerator Laboratoryyuyatsu@fnal.gov

PP0

Logical ”or” in Trajectory Recognition

Likelyhood function based on logical ”OR” transforms atrajectory recognition (by measured 3D points) in the taskof analysis of multi-extreme function of trajectory param-eters where each real trajectory corresponds to big maxi-mum at a background of small ones of noise and combina-torial nature.

Yuriy A. YatsunenkoFermi National Accelerator Laboratoryyuyatsu@fnal.gov