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All rights reserved © 2011, e-GEOS e-GEOS Via Cannizzaro 71 00156 Roma - Italy Redundant Phase Unwrapping and Integration of Finite Differences on a Sparse Multidimensional Domain: Theory and Validation Mario Costantini, Fabio Malvarosa, Federico Minati e-GEOS - an ASI/Telespazio Company mario.costantini@{e-geos.it; gmail.com}

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  • All rights reserved © 2011, e-GEOS

    e-GEOS

    Via Cannizzaro 7100156 Roma - Italy

    Redundant Phase Unwrapping and Integration of Finite Differences

    on a Sparse Multidimensional Domain: Theory and Validation

    Mario Costantini, Fabio Malvarosa, Federico Minati

    e-GEOS - an ASI/Telespazio Companymario.costantini@{e-geos.it; gmail.com}

  • All rights reserved © 2011, e-GEOS

    Introduction

    • We propose a robust finite difference integration and phase unwrapping approach

    • The reconstruction problem is formulated as the inversion of an overdetermined linear system of equations

    • Standard phase unwrapping techniques are comprised as particular cases

    • The proposed general formulation allows exploiting more information for a more robust solution:– Highly redundant phase unwrapping and finite difference integration– Multi-temporal phase unwrapping– Multi-baseline / multi-frequency phase unwrapping– Integration of external information (e.g. GPS)

    • Linear programming (LP) or quadratic programming (QP) problems with with L1 or L2 norm, respectively

    • Computationally efficient, even though slower than minimum cost flow [Costantini, 1996-1997] –[Costantini and Rosen, 1999]

    • Validation both on real and simulated interferometric SAR data confirm the validity of the approach

    • Integrated in our operational processing chain and used in massive productions

  • All rights reserved © 2011, e-GEOS

    Differences integration & phase unwrapping

    • In SAR interferometry two reconstruction problems on sparse domains (the coherent points or PS) are faced:– Phase unwrapping– Mean velocity and elevation reconstruction

    • Mathematically these problems are identical: integration of finite differences

    • The function is reconstructed by “integrating” preliminary estimates of nearest neighboring points differences

    • In general, the differences estimates are inconsistent, and the reconstructed values depend on the integration path

    • That is, the solution is over-determined, and can be determined, up to an additive constant, by minimizing, according to a given metric (L1, L2) the residuals of the different determinations

  • All rights reserved © 2011, e-GEOS

    What for a robust solution?

    • Increased over-determination by a highly redundant set of arcs (not only planar graphs)

    • Multi-dimensional information exploitation (not one-to-one correspondence equation-arc):– multi-temporal/acquisition– multi-frequency– multi-baseline– etc.

    • Further constraints based on external information (GPS, etc.)

  • All rights reserved © 2011, e-GEOS

    The proposed novel approach includes standard techniques as special case, but allows obtaining a solution more robust to noise and outliers by exploiting redundant information obtained working with more pairs of close points (not only nearest neighbors).

    The integration along a spanning tree is equivalent to the one-dimensional case.

    The standard technique solve the phase unwrap (and the finite difference integration) problem

    starting from a set of differences between nearest neighbors.

    • 1st level neighbors

    • 3rd level neighbors

    • 2nd level neighbors

    Phase unwrap and finite difference integration: two dimensional example

    Connecting nearest neighbors allows exploiting a new condition: the integration along any cycle must be zero.

    Exploitation of highly redundant information for accuracy and robustness

  • All rights reserved © 2011, e-GEOS

    Mathematical formulation of finite difference integration and phase unwrapping problem

    Quadratic programming (QP) problem with the L2 norm (p = 2)•

    Linear programming (LP) problem with the L1 norm (p = 1)– more robust to error spreading– integer multiples of 2p in phase unwrapping (easily proved

    using results of graph theory)

    estimated differences on the graph arcs

    reconstructed values on the graph nodes

    arcs (pairs of points)

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    ijijji

    Aji

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    ijijij

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    equation residualsweights

  • All rights reserved © 2011, e-GEOS

    Highly redundant phase unwrapping and finite difference integration

    • 1st level neighbors

    • 2nd level neighbors

    • 3rd level neighbors

    • Not a planar graph• Easy to add redundant arcs in the proposed formulation:

    – one equation (and corresponding residual) for each arc

    • PERSISTENT SCATTERE PAIR (PSP) ARCS GIVE THE BEST RESULTS: arcs are chosen based on their coherence

    • Another advantage of this formulation is the possibility of integrating external information (e.g. GPS measurements)

  • All rights reserved © 2011, e-GEOS

    Equivalent formulation based on “irrotationality constraints”

    • With the L1 norm, linear programming (LP) problem [Costantini, 1996-98; Costantini et al., ’02]

    • With the L1 norm and planar graphs, minimum cost flow problem on a network [Costantini, ’96-’98; Costantini and Rosen, ’99]

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    integration on a tree

    • Consider a simple case: a triangle

    • In the case of a general graph it is sufficient to choose a basis of the cycle space (i.e. the space spanned by all closed paths) and to sum the equations of each cycle (for a planar graph the Delaunay triangles constitute a cycle basis):

  • All rights reserved © 2011, e-GEOS

    Multi-temporal/multi-layer phase unwrapping

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    • The redundant finite difference integration and phase unwrapping method previously discussed is valid for generally sparse data on multidimensional domains (also 3D).

    • In a less general form without highly redundant arcs was already proposed by us [Costantini et al., 2002].

    • Not suitable for non-isotropic multi-dimensional spaces. The considered space-time domain is highly non-isotropic due to atmospheric and orbital artifacts.

    • The general formulation we propose makes possible to overcome the problem by considering double differences (in time and space)

    • Joint unwrapping of multitemporal interferometric phases (zero residue both in space and time cycles)

  • All rights reserved © 2011, e-GEOS

    Examples of graphs in temporal domain (1)

    Redundant consecutive

    • In the temporal domain, different graph configurations can be typically considered

    • Given n images, the standard approach consisting in n

    – 1 independent 2D phase unwrapping corresponds to consider a tree in the temporal domain

    • By considering, instead of a simple tree, a graph with a redundant number of arcs it is possible to obtain a solution more robust to outliers and noise

    • The temporal arcs (k, l)

    A2 should short so that the deviations δijkl

    are small on average

    • The most obvious configuration is a graph obtained by considering all arcs between nodes temporally close, up to a certain distance (Redundant consecutive configuration)

    Nodes represent the acquisitions

    The arcs connecting the consecutive nodes are drawn with solid lines (red).

    Dotted lines (blue) represent the arcs needed to obtain a graph with edge connectivity 2

    Dashed lines (violet) represent the arcs needed to obtain a graph with edge connectivity 3

  • All rights reserved © 2011, e-GEOS

    Examples of graphs in temporal domain (2)

    Maximum connectivity Redundant unique master

    • If a model of the phase temporal evolution valid for the whole time interval is available (e.g. obtained by calculating the temporal coherence in PS interferometry), preliminary estimates such that the deviations δijkl

    are small can be found for any temporal arc

    • The temporal arcs in A2

    should ideally connect any acquisition time with all the others in order to obtain the best solution

    • The resulting minimization problem could be very large and require too much computational time

    Trade-off is requested

    The solid lines (red) represent the minimal set of arcs needed to obtain a graph of edge connectivity 2 (a cycle).

    The dotted lines (blue) represent the minimal sets of arcs to add to the cycle in order to obtain graphs with connectivity 3.

    The solid lines (red) define a unique master graph of edge connectivity 1

    It is obtained by joining a “maximum connectivity” and a “unique master” configuration.

    The dashed lines (violet) represent the minimal sets of arcs to add to the cycle in order to obtain graphs with connectivity 4

    The union set of both is the minimal set that gives connectivity 5

    Adding the dotted lines (blue) a graph with connectivity 3 is obtained

    Adding also the dashed lines (violet) the connectivity becomes 5

    More arcs than maximum connectivity configuration

    “Unique master” configuration is useful to avoid the error integration in the time.

  • All rights reserved © 2011, e-GEOS

    Multi-baseline/multi-frequency phase unwrapping

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    • Multiple interferometric pairs are considered with slightly different baselines (multi-baseline interferometry) or at different frequencies (wide-band interferometry).

    • Same formulation as multi-temporal phase unwrapping, but an additional property holds (the interferometric phase is proportional to the baseline or the frequency):

    • A unique function g to be reconstructed for all frequencies/baselines:

  • All rights reserved © 2011, e-GEOS

    Processing is feasible

    • The differences integration (mean velocity and elevation reconstruction / phase unwrapping) problem reduces to:– Linear programming (LP) corresponding to L1 norm– Quadratic programming (QP) corresponding to L2 norm

    • Computationally efficient algorithms exist (even though slower than MCF)

    • The proposed redundant LP/QP method for differences integration is operational in our production chains and extensively tested and used also for massive productions

  • All rights reserved © 2011, e-GEOS

    Validation

  • All rights reserved © 2011, e-GEOS

    • Given a triplet of SAR images a, b, c, let fab

    , fbc

    and fac

    be the unwrapped interferometric phases of the pairs (a, b), (b, c), (a, c).

    • The consistency check is verified if the relation fab

    + fbc

    - fac

    = 0 holds.

    • We performed the test on the phase unwrapping results obtained on a stack of 34 ENVISAT SAR acquisitions (2002- 2010) over Abruzzo, Italy (track 129, frame 855), and a stack of 38 ENVISAT SAR acquisitions 2002-2010) over Sicily, Italy (track 172, frame 744).

    • The interferometric phases to be unwrapped were defined on a set of sparse points corresponding to the persistent scatterers (PS) identified by the PSP method

    Consistency check

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    Results of the consistency check

    Unwrapped phase obtained with Minimum cost flow (MCF) algorithm

    Unwrapped phase obtained with 2D LP redundant phase unwrapping algorithm (with arcs up to the 3rd neighbors)

    The solution of the multi-temporal phase unwrapping method clearly does not have inconsistencies at all, being the consistency conditions enforced in the problem equations

    Arc redundancy Phase unwrapping inconsistency

    Nearest neighbors (MCF) 3.1%

    2nd

    neighbors 2.7%

    3rd

    neighbors 2.5%

    PSP arcs 1.8%

    Multi-temporal 0 % (by construction)

    The best results were achieved when using the redundant graph built with the persistent scatterer pairs (PSP) method, due to the fact that in this case the pairs of points expressing redundant conditions are chosen based on their temporal coherence and not only by their spatial proximity.

  • All rights reserved © 2011, e-GEOS

    • We tested algorithm on portions of a stack of real ENVISAT SAR images (track 172, frame 744) over Sicily, Italy

    Redundant 2D and multi-temporal phase unwrapping experiments on real data

    • We considered the three different temporal graph configurations previously defined: redundant consecutive, maximum connectivity, redundant unique master

    • We considered spatial graphs with arcs connecting up to 3rd neighbors in the Delaunay triangulation (i.e. points connected by a path of up to three triangle edges)

    • Two experiments were performed:1. To check the robustness of the algorithm with respect to perturbations of the

    weights in the objective function of the problem2. To check the converge to a steady solution increasing the redundancy level. As

    reference solution we considered the statistical mode of the unwrapped phases of all the experimented configurations

  • All rights reserved © 2011, e-GEOS

    Experiment 1 on real data: robustness check

    Percentages of pixels unwrapped differently when the weights of the problem are perturbed with uniformly distributed noise in the range [-0.2, 0.2]

    • Notice that unitary temporal connectivity corresponds to 2D LP redundant phase unwrapping results

    • As expected, the stability of the solution tends to increase with the level of redundancy in the spatial and/or temporal domains

    • The improvement with respect to the MCF algorithm reaches 72% by exploiting only spatial redundancy, and 89% by exploiting both spatial and temporal redundancies

    0,010

    0,100

    1,000

    10,000

    0 2 4 6 8 10 12 14 16

    Temporal connectivity

    Diff

    eren

    ces

    %

    Consec. - N1 Max Conn. - N1 UM - N1 Consec. - N2

    Max Conn. - N2 UM - N2 UM - N3 Consec. - N3

    UM, Max Conn. and Consec. denote the (redundant) unique master, maximum connectivity and consecutive temporal graph configurations.

    N1, N2 and N3, denote the cases when the spatial arcs connect 1st, 2nd, and 3rd neighbors in the Delaunay triangulation.

  • All rights reserved © 2011, e-GEOS

    Experiment 2 on real data: converge check

    • Notice that unitary temporal connectivity corresponds to 2D LP redundant phase unwrapping results

    • As expected, the differences tend to zero, i.e. the phase unwrapping solutions converge to a common steady solution with the increase of the redundancy level0,100

    1,000

    10,000

    100,000

    0 2 4 6 8 10 12 14 16

    Temporal connectivity

    Diff

    eren

    ces

    %

    Consec. - N1 Max Conn. - N1 UM - N1 Consec. - N2

    Max Conn. - N2 UM - N2 UM - N3 Consec. - N3

    Percentages of pixels unwrapped differently with respect to a reference solution (the statistical mode of the phase unwrapping results obtained in all the configurations)

    UM, Max Conn. and Consec. denote the (redundant) unique master, maximum connectivity and consecutive temporal graph configurations.

    N1, N2 and N3, denote the cases when the spatial arcs connect 1st, 2nd, and 3rd neighbors in the Delaunay triangulation.

  • All rights reserved © 2011, e-GEOS

    Redundant 2D and multi-temporal phase unwrapping experiment on simulated data

    Percentage of phase unwrapping errors in an experiment with a stack of simulated ENVISAT SAR images as a function of the temporal connectivity

    0,10

    1,00

    10,00

    100,00

    0 2 4 6 8 10 12 14 16

    Temporal connectivity

    Diff

    eren

    ces

    %

    Consec. - N1 Max Conn. - N1 UM - N1 Consec. - N2

    Max Conn. - N2 UM - N2 UM - N3 Consec. - N3

    • The phases were simulated assuming absence of phase variation in time, and were characterized by random noise plus spatial correlated artifacts representing atmosphere and orbital errors.

    • The magnitude of the phase noise was simulated according to the measured values of the temporal coherence associated to each PS in the real data

    • Spatial correlated artifacts: planar surfaces with slope coefficients uniformly distributed in the range [-π/5000,+π/5000] rad/pixel in order to reproduce a low degree of coherence between distant points as in real data

    • The measured percentages of wrongly unwrapped phases confirm that the exploitation of redundant information in the spatial and/or in the temporal domain makes for a better solution.

    The improvement with respect to the MCF algorithm reaches 83%.

  • All rights reserved © 2011, e-GEOS

    Multi-baseline phase unwrapping experiment on simulated data

    • Six COSMO-SkyMed Himage SAR data (2009-2010) acquired in HH polarization with an incidence angle of about 40° on a region in Ecuador characterized by steep mountains, were used for the test

    • The data formed three interferometric pairs, the images of each pair being acquired at consecutive days (tandem-like acquisitions)

    • Simulated interferometric phases were obtained by using the real acquisition parameters and an available digital elevation model (res. 10 m x 10 m) of the region

    Average (radians)

    Std. dev (radians)

    90% conf. (radians)

    MCF unwrapping of 60

    m baseline phases

    0.00 5.59 9.31

    MCF unwrapping of 120

    m baseline phases

    0.00 2.34 3.64

    MCF unwrapping of 350

    m baseline phases

    -0.15 2.72 5.24

    Multi-baseline phase unwrapping

    -0.01 2.02 3.20

    • We considered several realizations of three interferograms with perpendicular baselines of 60 m, 120 m and 350 m

    • The noise affecting the measured phases was simulated based on the coherence measured on the real interferometric pairs

    • Before phase unwrapping, in order to reduce the fringe frequency, the interferometric phases were flattened using a DEM of much lower resolution (100 m x 100 m) than the one used for the simulation

  • All rights reserved © 2011, e-GEOS

    Application examples

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    COSMO-SkyMed and ENVISAT PSP IFSAR analysis over Beijing, China

  • All rights reserved © 2011, e-GEOS

    ENVISAT and COSMO-SkyMed acquisitions

    on Beijing

    ENVISAT

    • Track 2218 Frame 2805

    • Ground resolution 5 m x 25 m

    • Polarization VV

    • Incidence angle ~23°

    • Descending pass

    • Analyzed period: June 2003 – May 2010

    • Number of acquisitions: 49

    COSMO-SKYMED

    • Stripmap H4-0A mode

    • Ground resolution 3 m x 3 m

    • Polarization HH

    • Incidence angle 20.06°

    • Right looking, descending

    • Analyzed period: Mar. 2008 – Jun. 2010

    • Number of acquisitions: 31

  • All rights reserved © 2011, e-GEOS

    Beijing ENVISAT 2003-2010 PSP-IFSAR analysis

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    Chaoyang District, Beijing COSMO-SkyMed 2008-2010 PSP-IFSAR

    analysis

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    COSMO-SkyMed vs ENVISAT PSP-IFSAR analysis

  • All rights reserved © 2011, e-GEOS

    COSMO-SkyMed vs ENVISAT

    PS mean velocities: area 1CSK vs ENVISAT displacement

    -170

    -165

    -160

    -155

    -150

    -145

    -140

    -135

    -130

    -125

    -120

    -115

    -110

    -105

    -100

    11/14/07 02/22/08 06/01/08 09/09/08 12/18/08 03/28/09 07/06/09 10/14/09 01/22/10 05/02/10 08/10/10

    Time (days)

    Dis

    plac

    emen

    t (m

    m)

    ENVISAT

    COSMO

  • All rights reserved © 2011, e-GEOS

    The China World Trade Center,Beijing COSMO-SkyMed 2008-2010 PSP-IFSAR

    analysis 3D view

  • All rights reserved © 2011, e-GEOS

    Validation with optical leveling from

    Beijing Institute of Surveying and Mapping

    No. Leveling(mm)

    PSP(mm)

    Leveling-PSP (mm)

    1 -3 -2 -1

    2 -5 -3.4 -1.6

    3 -1 -3.5 2.5

    4 -6 -3.4 -2.6

    5 -9 -7.8 -1.2

    6 -7 -3.4 -3.6

    Mean = -1.2 mm, Std dev. = 1.9 mm Velocity accuracy: 0,5 mm/year in 4 years

    COSMO-SkyMed PSP-IFSAR ground deformation measurements:

    • Millimetric accuracy (almost an order of magnitude more precise than with C-band Envisat data)

    • Up to more than 30 thousand PS/km2 with stripmap data (two orders of magnitude more than with Envisat data)

    Comparison between PSP-IFSAR and optical leveling measurements march 2009 - march 2010.

    PLEASE VISIT TOMORROW POSTER SESSION FOR DETAILS

  • All rights reserved © 2011, e-GEOS

    Comparison ERS/COSMO-SkyMed

    PSPPSP--IFSAR processing IFSAR processing --

    ERS data ERS data (1992(1992--2000)2000)

    Descending passDescending pass

    PSPPSP--IFSAR processing IFSAR processing --

    CSK Stripmap data CSK Stripmap data (2008(2008--2010)2010)

    Descending passDescending pass

  • All rights reserved © 2011, e-GEOS

    A3A3-- NapoliNapoli-- SalernoSalerno

    Analisi interferometrica da dati COSMO-SkyMed Stripmap- Modalità ascending

    Periodo 2008-2010

    A3A3-- NapoliNapoli-- SalernoSalerno

    Analisi interferometrica da dati ENVISAT (fonte: PST) Modalità ascending

    Periodo 2002-2008

    Comparison Envisat/COSMO-SkyMed

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    Examples of COSMO-SkyMed PSP IFSAR analysis

    of subsidence along the Shanghai subway, China

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    COSMO-SkyMed acquisitions used for PSP-IFSAR analysis

    • Stripmap H4-0B acquisition mode

    • Ground resolution 3 m x 3 m

    • Polarization HH

    • Incidence angle 23.96°

    • Right looking, descending pass

    • Analyzed period: May. 2008 – Dec. 2009

    • Number of acquisitions: 36

  • All rights reserved © 2011, e-GEOS

    PSP-IFSAR Mean velocity Shanghai subway line 9

    COSMO-SkyMed May 2008 – Jun 2010

    Lujiabang Road

    Xiaonanmen

    Middle Yanggao Rd.

    Century Avenue

    Shangcheng Rd.

  • All rights reserved © 2011, e-GEOS

    Shanghai subway line 9 detail COSMO-SkyMed 2008–2010 PSP-IFSAR

    analysis

    Lujiabang Road

    Xiaonanmen

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    COSMO-SkyMed PSP IFSAR analysisof railway tracks in Russia

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    PSP-IFSAR application examples

    • E-Geos successfully completed a pilot project for the Russian Railway company (NIIAS/RZD) to assess the capabilities of PSP SAR interferometry in monitoring the railway track Adler-Tuapse

    • An operational monitoring service is currently in progress– Some preliminary results will be shown in the next slides

    COSMO-SkyMed Stripmap coverage of the area of interest

    Area of interest

    Black SeaBlack Sea

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    COSMO-SkyMed acquisitions used for PSP-IFSAR analysis

    • Stripmap HI-01 acquisition mode

    • Ground resolution 3 m x 3 m

    • Polarization HH

    • Incidence angle 26.65°

    • Right looking, descending pass

    • Analyzed period: Dec. 2008 – Sept. 2010

    • Number of acquisitions: 52

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    Landslides along the railway line PSP-IFSAR analysis 3D view

    Areas affected by landslides

    Railway

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    Landslides PS mean velocities 3D view

    Railway

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    Tuapse PSP-IFSAR analysis

    Harbor

    Areas affected by landslides

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    Tuapse Harbor PSP-IFSAR analysis

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    Tuapse landslide PSP-IFSAR analysis

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    PSP analysis of an industrial site

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    PSP analysis of an antenna

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    PSP analysis of a bridge, 3D view

    Railway

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    PST project

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    • The PST-A/2 project, commissioned by the Italian Ministry of the Environment, is a huge project aimed at providing terrain displacement measurements by SAR interferometry over an entire national territory (Italy, 300,000 Km2)

    • Analysis of the whole period covered by data available for interferometry: 1992–2000 (ERS) and 2003–2010 (Envisat)

    • Processing of the whole ESA ERS/Envisat archive over Italy (about 15,000 images), by TRE and e-GEOS

    • TO BE PROBABLY EXTENDED WITH COSMO-SKYMED DATA

    Some examples from a nation-wide PSI analysis project

    PLEASE VISIT TOMORROW POSTER SESSION FOR DETAILS

  • All rights reserved © 2011, e-GEOS

    Mean velocity(mm/year)

    < -9.0

    -9.0 - -7.0

    -5.0 - -3.0

    -3.0 - -1.0

    -1.0 - 10

    1.0 - 3.0

    5.0 - 7.0

    > 7.0

    -7.0 - -5.0

    3.0 - 5.0

    Italy 2003-2008 ENVISAT descending data (updated to 2010 - to be completed by

    beginning 2011)

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    Mean velocity(mm/year)

    < -9.0

    -9.0 - -7.0

    -5.0 - -3.0

    -3.0 - -1.0

    -1.0 - 10

    1.0 - 3.0

    5.0 - 7.0

    > 7.0

    -7.0 - -5.0

    3.0 - 5.0

    Italy 2003-2008 ENVISAT ascending data (updated to 2010 - to be completed by

    beginning 2011)

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    Romagna, Italy, subsidence monitoring ENVISAT 2003-2008 PSP-IFSAR analysis

    1992-2000 ERS DESC1992-2000 ERS ASC

    Mean Velocity (mm/year)

    < -9.0

    -8.99 - -7.00

    -4.99 - -3.00

    -2.99 - -1.00

    -0.99 - 1.00

    1.01 - 3.00

    3.01 - 5.00

    5.01 - 7.00

    > 7.0

    -6.99 - -5.00

    Water extraction

    Gas extraction

    Offshore platforms

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    Volcanic bradyseism, Naples region, Italy PSP-IFSAR analysis and validation

    Mean velocity(mm/year)

    < -9.0

    -9.0 - -7.0

    -5.0 - -3.0

    -3.0 - -1.0

    -1.0 - 1.0

    1.0 - 3.0

    5.0 - 7.0

    > 7.0

    -7.0 - -5.0

    3.0 - 5.0

    1995-2000 ERS

    > 7.0

    5.0 - 7.0

    3.0 - 5.0

    1.0 - 3.0

    -1.0 - 1.0

    -3.0 - -1.0

    -5.0 - -3.0

    -7.0 - -5.0

    -9.0 - -7.0

    < -9.0

    Mean velocity(mm/year)

    2002-2008 ENVISAT

    2000

    2050

    2100

    2150

    2200

    2250

    2300

    2350

    2400

    2450

    2500

    05/07/90 01/31/93 10/28/95 07/24/98 04/19/01 01/14/04 10/10/06 07/06/09 04/01/12

    Time

    Dis

    plac

    emen

    t (m

    m)

    Levelling

    ERS

    ENVISAT

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    Etna volcano ENVISAT (2003-2008) PSP-IFSAR analysis

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    Dam monitoring ENVISAT (2003-2008) PSP-IFSAR analysis

    -70

    -60

    -50

    -40

    -30

    -20

    -10

    0

    10

    20

    30

    1/9/2002 14/1/2004 28/5/2005 10/10/2006 22/2/2008 6/7/2009

    Time (days)

    Dis

    plac

    emen

    t (m

    m/y

    ear)

    -70

    -60

    -50

    -40

    -30

    -20

    -10

    0

    10

    20

    30

    1/9/2002 14/1/2004 28/5/2005 10/10/2006 22/2/2008 6/7/2009

    Time (days)

    Dis

    plac

    emen

    t (m

    m/y

    ear)

  • All rights reserved © 2011, e-GEOS

    Landslide PSP-IFSAR analysis

    2003-2008 ENVISAT ASC 2003-2008 ENVISAT DESC

    Using

    two

    acquistion

    geometries

    (ascending

    and descending) two

    components

    of

    the ground

    displacement

    are measured,

    and vertical

    and east-west

    displacemnts

    can be

    determined.

  • All rights reserved © 2011, e-GEOS

    Conclusion

    • We propose a robust finite difference integration and phase unwrapping approach

    • The reconstruction problem is formulated as the inversion of an overdetermined linear system of equations

    • Standard phase unwrapping techniques are comprised as particular cases

    • The proposed general formulation allows exploiting more information for a more robust solution:– Highly redundant phase unwrapping and finite difference integration– Multi-temporal phase unwrapping– Multi-baseline / multi-frequency phase unwrapping– Integration of external information (e.g. GPS)

    • Linear programming (LP) or quadratic programming (QP) problems with with L1 or L2 norm, respectively

    • Computationally efficient, even though slower than minimum cost flow [Costantini, 1996-1997] –[Costantini and Rosen, 1999]

    • Validation both on real and simulated interferometric SAR data confirm the validity of the approach

    • Integrated in our operational processing chain and used in massive productions

    PLEASE LOOK PAPER ON TGRS FOR FURTHER DETAILS

    Slide Number 1IntroductionDifferences integration & phase unwrappingWhat for a robust solution?Slide Number 5Mathematical formulation of finite difference integration and phase unwrapping problem Highly redundant phase unwrapping�and finite difference integrationEquivalent formulation based on “irrotationality constraints”Multi-temporal/multi-layer �phase unwrappingSlide Number 10Slide Number 11Multi-baseline/multi-frequency �phase unwrappingProcessing is feasibleSlide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23ENVISAT and COSMO-SkyMed acquisitions �on Beijing Beijing �ENVISAT 2003-2010 PSP-IFSAR analysisChaoyang District, Beijing�COSMO-SkyMed 2008-2010 PSP-IFSAR analysisCOSMO-SkyMed vs ENVISAT�PSP-IFSAR analysisCOSMO-SkyMed vs ENVISAT�PS mean velocities: area 1 The China World Trade Center,Beijing�COSMO-SkyMed 2008-2010 PSP-IFSAR analysis 3D viewValidation with optical leveling from�Beijing Institute of Surveying and Mapping Comparison ERS/COSMO-SkyMedSlide Number 32Slide Number 33COSMO-SkyMed acquisitions�used for PSP-IFSAR analysisPSP-IFSAR Mean velocity�Shanghai subway line 9�COSMO-SkyMed May 2008 – Jun 2010Shanghai subway line 9 detail�COSMO-SkyMed 2008–2010 PSP-IFSAR analysisSlide Number 37PSP-IFSAR application examplesCOSMO-SkyMed acquisitions�used for PSP-IFSAR analysisLandslides along the railway line � PSP-IFSAR analysis 3D viewLandslides�PS mean velocities 3D viewTuapse� PSP-IFSAR analysisTuapse Harbor�PSP-IFSAR analysisTuapse landslide� PSP-IFSAR analysisPSP analysis of an industrial site PSP analysis of an antennaPSP analysis of a bridge, 3D viewSlide Number 48Slide Number 49Slide Number 50Slide Number 51Romagna, Italy, subsidence monitoring�ENVISAT 2003-2008 PSP-IFSAR analysisVolcanic bradyseism, Naples region, Italy �PSP-IFSAR analysis and validationEtna volcano�ENVISAT (2003-2008) PSP-IFSAR analysisDam monitoring�ENVISAT (2003-2008) PSP-IFSAR analysisLandslide PSP-IFSAR analysisConclusion