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Compressed Sensing for Polarimetric SAR Tomography   E. Aguilera, M. Nannini and  A. Reigber
[object Object],[object Object],[object Object],[object Object],[object Object],Overview
[object Object],Tomographic SAR data acquisition azimuth ground range ,[object Object]
The tomographic data stack ,[object Object],M  images azimuth range
The tomographic data stack ,[object Object],azimuth range
The tomographic signal model: B = AX height B  : measurements A  : steering matrix X  : unknown reflectivity
What’s the problem? ,[object Object],[object Object],[object Object],[object Object]
Where does this work fit? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Elevation profile reconstruction A A MxN   : steering matrix X N   : unknown reflectivity B M   : stack of pixels height gnd. range azimuth
The compressive sensing approach ,[object Object],subject to Convex optimization problem
How many tracks? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
CS for vegetation mapping ? ,[object Object],[object Object],elevation amplitude = + + … +
Tomographic E-SAR Campaign ,[object Object],[object Object],[object Object],[object Object],[object Object],3,5 m ,[object Object]
[object Object],40 m 2 corner reflectors in layover Canopy and ground Ground 40 m Single Channel Compressive Sensing ,[object Object]
Normalized intensity – 40 m Beamforming   (23 passes, 3 x3 ) SSCS  ( 5  passes,  3x3 )
Multiple Signal Compressive Sensing ,[object Object],L  columns G HH azimuth range range azimuth M images
Polarimetric correlations ,[object Object],3L  columns G HH   G HV   G VV
Elevation profile reconstruction A MxN   : steering matrix HH   HV   VV Y Nx3L   : unknown reflectivities Mx3L   : stacks of pixels
Y Nx3L   : unknown reflectivity subject to Elevation profile reconstruction We look for a matrix with the least number of non-zero rows that matches the measurements
Mixed-norm minimization subject to Number of columns in  Y   (window size + polarizations) Probability of recovery failure  (Eldar and Rauhut, 2010)
SSCS (saturated) MSCS (span saturated) MSCS (polar) MSCS (span) Layover recovery with CS
Beamforming   (23 passes, 3 x3 ) SSCS  ( 5  passes,  3x3 ) MSCS  ( 5  passes,  3x3 ) MSCS  (pre-denoised)  ( 5  passes,  3x3 ) Layover recovery with CS
Volumetric Imaging ,[object Object],[object Object],40 m
Volumetric Imaging ,[object Object],[object Object],40 m
Volumetric Imaging ,[object Object],[object Object],40 m
Towards a “realistic” sparse vegetation model ,[object Object],elevation amplitude ,[object Object]
Sparsity in the wavelet domain ,[object Object],[object Object],[object Object],ground canopy ground canopy 0.5 1 0 0.5 1 0
Elevation profile reconstruction s.t. ,[object Object],[object Object],[object Object],synthetic aperture
Volumetric Imaging in Wavelet Domain ,[object Object],[object Object],40 m
Volumetric Imaging in Wavelet Domain ,[object Object],[object Object],40 m
Conclusions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Convex optimization solvers ,[object Object],[object Object]

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DCS-IGARSS11_v2-aguilera.ppt

  • 1. Compressed Sensing for Polarimetric SAR Tomography E. Aguilera, M. Nannini and A. Reigber
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  • 6. The tomographic signal model: B = AX height B : measurements A : steering matrix X : unknown reflectivity
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  • 9. Elevation profile reconstruction A A MxN : steering matrix X N : unknown reflectivity B M : stack of pixels height gnd. range azimuth
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  • 15. Normalized intensity – 40 m Beamforming (23 passes, 3 x3 ) SSCS ( 5 passes, 3x3 )
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  • 18. Elevation profile reconstruction A MxN : steering matrix HH HV VV Y Nx3L : unknown reflectivities Mx3L : stacks of pixels
  • 19. Y Nx3L : unknown reflectivity subject to Elevation profile reconstruction We look for a matrix with the least number of non-zero rows that matches the measurements
  • 20. Mixed-norm minimization subject to Number of columns in Y (window size + polarizations) Probability of recovery failure (Eldar and Rauhut, 2010)
  • 21. SSCS (saturated) MSCS (span saturated) MSCS (polar) MSCS (span) Layover recovery with CS
  • 22. Beamforming (23 passes, 3 x3 ) SSCS ( 5 passes, 3x3 ) MSCS ( 5 passes, 3x3 ) MSCS (pre-denoised) ( 5 passes, 3x3 ) Layover recovery with CS
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Notes de l'éditeur

  1. In our model, we try to approximate the ground and canopy components by a summation of sparse profiles. This is quite different to conventional methods which consider each term of the summation to be non-sparse. Okay, so, during this presentation we’ll be concerned with trying to find these terms. The question is: where do we get these terms from?
  2. Here we can compare the CS approach for single signals and for multiple signals. At first glance, they look the same, but we can notice that the bottom image is definitely sharper / has more quality. In addition, if we do a close-up, we can see the noise has been reduced.
  3. Here we can compare the CS approach for single signals and for multiple signals. At first glance, they look the same, but we can notice that the bottom image is definitely sharper / has more quality. In addition, if we do a close-up, we can see the noise has been reduced.
  4. Here we can compare the CS approach for single signals and for multiple signals. At first glance, they look the same, but we can notice that the bottom image is definitely sharper / has more quality. In addition, if we do a close-up, we can see the noise has been reduced.
  5. Here we can compare the CS approach for single signals and for multiple signals. At first glance, they look the same, but we can notice that the bottom image is definitely sharper / has more quality. In addition, if we do a close-up, we can see the noise has been reduced.
  6. Here we can compare the CS approach for single signals and for multiple signals. At first glance, they look the same, but we can notice that the bottom image is definitely sharper / has more quality. In addition, if we do a close-up, we can see the noise has been reduced.