DCS-IGARSS11_v2-aguilera.ppt

4,925 views
4,867 views

Published on

Published in: Technology, Business
0 Comments
1 Like
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total views
4,925
On SlideShare
0
From Embeds
0
Number of Embeds
1,096
Actions
Shares
0
Downloads
33
Comments
0
Likes
1
Embeds 0
No embeds

No notes for slide
  • 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?
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • DCS-IGARSS11_v2-aguilera.ppt

    1. 1. Compressed Sensing for Polarimetric SAR Tomography E. Aguilera, M. Nannini and A. Reigber
    2. 2. <ul><li>Polarimetric SAR tomography </li></ul><ul><li>Compressive sensing of single signals </li></ul><ul><li>Multiple signals compressive sensing: Exploiting correlations </li></ul><ul><li>Compressive sensing for volumetric scatterers </li></ul><ul><li>Conclusions </li></ul>Overview
    3. 3. <ul><li>M parallel tracks for 3D imaging </li></ul>Tomographic SAR data acquisition azimuth ground range <ul><li>Side-looking illumination at L-Band </li></ul>
    4. 4. The tomographic data stack <ul><li>Our dataset is a stack of M two-dimensional SAR images per polarimetric channel </li></ul>M images azimuth range
    5. 5. The tomographic data stack <ul><li>Projections of the reflectivity in the elevation direction are encoded in M pixels (complex valued) </li></ul>azimuth range
    6. 6. The tomographic signal model: B = AX height B : measurements A : steering matrix X : unknown reflectivity
    7. 7. What’s the problem? <ul><li>High resolution and low ambiguity require a large number of tracks: </li></ul><ul><li>Expensive and time consuming </li></ul><ul><li>Sometimes infeasible </li></ul><ul><li>Long temporal baselines affect reconstruction </li></ul>
    8. 8. Where does this work fit? <ul><li>Beamforming (SAR tomography): </li></ul><ul><ul><li>Beamforming (Reigber, Nannini, Frey) </li></ul></ul><ul><ul><li>Adaptive beamforming (Lombardini, Guillaso) </li></ul></ul><ul><ul><li>Covariance matrix decomposition (Tebaldini) </li></ul></ul><ul><li>Physical Models (SAR interferometry): </li></ul><ul><ul><li>PolInSAR (Cloude, Papathanassiou) </li></ul></ul><ul><ul><li>PCT (Cloude) </li></ul></ul><ul><li>Compressed sensing (SAR tomography) </li></ul><ul><ul><li>Single signal approach (Zhu, Budillon) </li></ul></ul><ul><ul><li>Multiple signal/channel approach </li></ul></ul>
    9. 9. Elevation profile reconstruction A A MxN : steering matrix X N : unknown reflectivity B M : stack of pixels height gnd. range azimuth
    10. 10. The compressive sensing approach <ul><li>We look for the sparsest solution that matches the measurements </li></ul>subject to Convex optimization problem
    11. 11. How many tracks? <ul><li>In theory: </li></ul><ul><li>take measurements </li></ul><ul><li>frequencies selected at random </li></ul><ul><li>In practice: </li></ul><ul><li>we can use our knowledge about the signal and sample less: </li></ul><ul><li>low frequency components seem to do the job! </li></ul>
    12. 12. CS for vegetation mapping ? <ul><li>The elevation profile can be approximated by a summation of sparse profiles </li></ul><ul><li>Different to conventional models (non-sparse). And probably a bad one… </li></ul>elevation amplitude = + + … +
    13. 13. Tomographic E-SAR Campaign <ul><li>Testsite: Dornstetten, Germany </li></ul><ul><li>Horizontal baselines: ~ 20m </li></ul><ul><li>Vertical baselines: ~ 0m </li></ul><ul><li>Altitude above ground: ~ 3800m </li></ul><ul><li># of baselines: 23 </li></ul>3,5 m <ul><li>2 corner reflectors in layover and ground </li></ul>
    14. 14. <ul><li>CAPON using 23 tracks (13x13 window) = ground truth </li></ul>40 m 2 corner reflectors in layover Canopy and ground Ground 40 m Single Channel Compressive Sensing <ul><li>CS using only 5 tracks </li></ul>
    15. 15. Normalized intensity – 40 m Beamforming (23 passes, 3 x3 ) SSCS ( 5 passes, 3x3 )
    16. 16. Multiple Signal Compressive Sensing <ul><li>Assumption: adjacent azimuth-range positions are likely to have targets at about the same elevation </li></ul>L columns G HH azimuth range range azimuth M images
    17. 17. Polarimetric correlations <ul><li>We can further exploit correlations between polarimetric channels </li></ul>3L columns G HH G HV G VV
    18. 18. Elevation profile reconstruction A MxN : steering matrix HH HV VV Y Nx3L : unknown reflectivities Mx3L : stacks of pixels
    19. 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. 20. Mixed-norm minimization subject to Number of columns in Y (window size + polarizations) Probability of recovery failure (Eldar and Rauhut, 2010)
    21. 21. SSCS (saturated) MSCS (span saturated) MSCS (polar) MSCS (span) Layover recovery with CS
    22. 22. Beamforming (23 passes, 3 x3 ) SSCS ( 5 passes, 3x3 ) MSCS ( 5 passes, 3x3 ) MSCS (pre-denoised) ( 5 passes, 3x3 ) Layover recovery with CS
    23. 23. Volumetric Imaging <ul><li>Single signal CS (5 tracks) </li></ul><ul><li>Multiple signal CS (5 tracks) </li></ul>40 m
    24. 24. Volumetric Imaging <ul><li>Single signal CS (5 tracks) </li></ul><ul><li>Multiple signal CS (5 tracks) </li></ul>40 m
    25. 25. Volumetric Imaging <ul><li>Polarimetric Capon beamforming (5 tracks) </li></ul><ul><li>Multiple signal CS (5 tracks) </li></ul>40 m
    26. 26. Towards a “realistic” sparse vegetation model <ul><li>Canopy and ground component </li></ul>elevation amplitude <ul><li>Possible sparse description in wavelet domain! </li></ul>
    27. 27. Sparsity in the wavelet domain <ul><li>Daubechies wavelet example: </li></ul><ul><ul><ul><li>4 vanishing moments </li></ul></ul></ul><ul><ul><ul><li>3 levels of decomposition </li></ul></ul></ul>ground canopy ground canopy 0.5 1 0 0.5 1 0
    28. 28. Elevation profile reconstruction s.t. <ul><li>Additional regularization </li></ul><ul><li>L1 norm of wavelet expansion </li></ul><ul><li>( W : transform matrix) </li></ul>synthetic aperture
    29. 29. Volumetric Imaging in Wavelet Domain <ul><li>Fourier beamforming using 23 tracks (23x23 window) </li></ul><ul><li>Wavelet-based CS (5 tracks) </li></ul>40 m
    30. 30. Volumetric Imaging in Wavelet Domain <ul><li>Fourier beamforming using 23 tracks (23x23 window) </li></ul><ul><li>Wavelet-based CS (5 tracks) </li></ul>40 m
    31. 31. Conclusions <ul><li>Single signal CS: </li></ul><ul><ul><li>High resolution with reduced number of tracks </li></ul></ul><ul><ul><li>Recovers complex reflectivities but polarimetry problematic </li></ul></ul><ul><ul><li>Model mismatch is not catastrophic (CS theory) </li></ul></ul><ul><ul><li>It’s time-consuming (Convex optimization) </li></ul></ul><ul><li>Multiple signal CS: </li></ul><ul><ul><li>Polarimetric extension of CS </li></ul></ul><ul><ul><li>Higher probability of reconstruction, less noise </li></ul></ul><ul><ul><li>More robust for distributed targets </li></ul></ul><ul><ul><li>Vegetation reconstruction in the wavelet domain </li></ul></ul>
    32. 32. Convex optimization solvers <ul><li>CVX ( Disciplined Convex Programming) : http://cvxr.com/cvx / </li></ul><ul><li>SEDUMI: http://sedumi.ie.lehigh.edu / </li></ul>

    ×