project: hybrid fluorescence molecular tomography … · 2011-05-02 · project: hybrid...

Project: Hybrid Fluorescence Molecular Tomography (FMT) – X-rayProject: Hybrid Fluorescence Molecular Tomography (FMT) X rayComputed Tomography (XCT) method and system

Work Package: FMT inversions with image priors

T Correia, T Rudge, V Soloviev, A Zacharopoulos and S Arridge

Deliverable 1: To quantitatively examine optimal inversion methods based on experimental data.

Deliveravle 2: To develop user-friendly software for inversion of FMT-XCT data based on a-priory inversion

D1: To quantitatively examine optimal inversion methods based on experimental data.

1 FMT inversion using XCT image priors

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1. FMT inversion using XCT image priors

Forward problem: )(xFy y

ex

fluo

yy

y measured data (fluorescence and excitation)

linear forward operator computed using a finite element method (FEM). JxxF )( p p g ( ))(

Inverse problem:

Prior term

WxJxyxE 2

21)(

Prior term - - regularisation parameter- prior function

minimise

xxLyJxJxE T )()( Anisotropic diffusion prior


1 1 Anisotropic diffusion

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xxgxWxxxL ref

)( W – anatomical prior

1.1. Anisotropic diffusion

gt ref

)( pg – edge-preserving function or diffusivity (e.g. Perona Malik, Total Variation, Huber andTukey)T – threshold parameter

21'

xx

xxg

1

Txx

Explicit update scheme:

Semi-implicit update scheme:

ki

ki

ki

ki xxtLxx )(1

1

Small step size more iterations

Discrete formulation:

1 kkkk gg

ki

ki

ki xxtLIx 11 )( Large step few iterations

)(2

1

2ij

ki

kj

ijki

ki xx

hgg

txx


1 1 Anisotropic diffusion

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1.1. Anisotropic diffusion

Smooths homogeneous regions whilst preserving edgesg

2x Anisotropic diffusion

Fluorescence example: 2x Anisotropic diffusion ...with anatomical prior


1 2 Image Reconstruction

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1. 2. Image Reconstruction

If is linear the solution can be obtained using:

yJxJJx TT 1)(

However, the anisotropic diffusion prior is nonlinear.A two-step method is used to obtain the solution:

Step 1: Image reconstruction without anisotropic priorStep 1: Image reconstruction without anisotropic prior

Step 2: Apply the anisotropic diffusion prior to the image obtained in Step 1

S d t i l d i G i li i tiSecond step is solved using a Gaussian elimination algorithm

Wavelet data compression


2 Simulations

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2. Simulations

•Digimouse atlas used to generate a mouse mesh

•Fluorescent target: r=1.75 mm h=1mm-1

•Liver: a = 0.035 mm-1 ’s= 0.68 mm-1

Other tissue: a = 0.01 mm-1 ’s= 0.8 mm-1a s

•16 projections

•1% Gaussian noise

•nwavelets =12 8


2 1 Simulation results

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2.1 Simulation results

Zero-order Tikhonov Total variation Perona-Malik Perona-Malik exp Bayesian


3 Phantom 1

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3. Phantom 1

CT + fluo data CCD camera

Partner 5•Slab phantom

• a = 0.01 mm-1 ’s= 0.8 mm-1X-ray tube X-ray detector

a s

•Capillary r=0.5mm

•2 L Alexa Fluor 680

•42 projections

•nwavelets = 128Laser diode


3 1 Phantom 1 results

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3.1. Phantom 1 results

Zero-order Tikhonov Total variation Perona-Malik

Perona-Malik exp Bayesian


4 Phantom 2

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4. Phantom 2 Partner 1

• a = 0.01 mm-1 ’s= 0.8 mm-1

•500nM Alexa Fluor 750

•Total of 162 projections, but only 18 were used in the reconstructions18 were used in the reconstructions

•nwavelets = 128

Zero-order Tikhonov Perona-Malik

D1: To quantitatively examine optimal inversion methods based on experimental data.D1: To quantitatively examine optimal inversion methods based on experimental data.

5 Mouse 1

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5. Mouse 1

Partner 1

•Brain tumour

• dye concentration ?

•Total of 184 projections, but only 29 were used in the reconstructions

xx29 were used in the reconstructions

•nwavelets = 128


5 1 Mouse 1 results

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5.1 Mouse 1 resultsZero-order Tikhonov Perona-Malik

Perona-Malik exp Bayesian


6 Mouse 2

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6. Mouse 2

Partner 5

•Capillary r=0.5mm inserted in the esophagus

•2 L Alexa Fluor 680

•56 projections

•nwavelets = 128x x


6 Mouse 2 results

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6. Mouse 2 results

Zero-order Tikhonov Perona-Malik

D2: To develop user-friendly software for inversion of FMT-XCT data based on a-priory inversion

1 Software

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1. Software

Matlab-based software that reconstructs FMT images using prior information

Requiresd software packages:TOAST http://web4.cs.ucl.ac.uk/research/vis/toast/ or from the project website http://www.fmt-xct.eu/transfer/) Stanford Wavelab http://www-stat.stanford.edu/~wavelab/

Add the software folder to your Matlab path andtype:>> FMT XCT UCL>> FMT_XCT_UCL


2 How to use

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2. How to use

HELP!


2 How to use

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2. How to use


2 How to use

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2. How to use

Mesh: * msh file Gnerated from the CT imagesMesh: .msh file. Gnerated from the CT images.

QM: *.qm file. Source and CCD camera positions

Fluorescence data: * mat * jpg * tiff Dimensions must be 128 x 128 xFluorescence data: .mat, .jpg, .tiff.... Dimensions must be 128 x 128 xnumber of projections

Excitation data: *.mat, *.jpg, *.tiff.... Dimensions must be 128 x 128 x numberof projectionsof projections

CT: *.mat, *.jpg, *.tiff.... Dimensions must be 128 x 128 x 100.. Previouslysmoothed


2 How to use

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2. How to use

Tikhonov: Select a function: TikhonovTotal VariationPerona-Malikexponential Perona-MalikHuberT kTukeyBayesian

Threshold: threshold T of the edge preserving function

Step size: <50, controls the influence of the prior

Iterations: <20, number of iterations of step 2

CT threshold: threshold value used to find the edges of the anatomical prior.Image showing the edges is displayed.


2 How to use

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2. How to useProjection pixel size: pixel size of the optical images

Hyperparameter: regularisation parameter. Insert manually or calculate using the L-curve ?yp p g p y g

Number of wavelets: number of wavelet coefficients to keep.

Display slice: Slice displayed during the reconstruction. p y p y g

Iterations: number of iterations in the reconstruction process

Without CT prior? check to reconstruct without anatomical priorp p

Calculate Jacobian?:

unckeck to load Jacobian and data filescheck to calculate a new compressed Jacobian and data unckeck to load Jacobian and data files

or load files with the optical properties


2 How to use

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2. How to use

Edges of the anatomical prior

Image reconstructed using zero-order Tikhonov

Image reconstructed using the anisotropic diffusion prior

Final reconstruction: scroll through slices

Conclusions

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Conclusions

Images reconstructed using the anisotropic better than simple Tikhonov regularisation

Reconstructions within seconds

The Jacobian calculations is the most time consuming step of the image reconstructions. It depends on the number of projections and wavelets used

A k l d tAcknowledgments

LIM Madrid

Dr. Juan Abascal

IBMI Munich

Angelique Ale

Juan Aguirre

g

Maximilian Koch

Alejandro Sisniega

Judit Chamorro

project: hybrid fluorescence molecular tomography … · 2011-05-02 · project: hybrid...

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