Application of Polarimetric SAR to Earth Remote Sensing<br />Jakob van Zyl and Yunjin Kim<br />Jet Propulsion Laboratory<b...
Overview<br />Polarimetric SAR data are becoming more available, both in single pass and interferometric form<br />Because...
                  Basic Tools: Polarization Signature<br />The polarization Signature is a simple graphical way to display...
Polarization Signatures  A New Perspective<br />
Dihedral Corner Reflector<br />
Rotated Dihedral<br />
                 Three Orthogonal Scatterers<br />Trihedral                                          Dihedral		 Rotated Di...
                Effect of Phase Calibration Error<br />No Error<br />45 Degrees<br />90 Degrees<br />180 Degrees<br />135 ...
               Effect Of Co-Channel Imbalance<br />Signatures are distorted.  Co-pol nulls are in the S1-S3 plane<br />
Dipole Orientation<br />Horizontal                                     45 Degrees                                  Vertica...
What do we Have Here?<br />
Polarization Synthesis<br />
Check Signatures<br />
Signature Analysis<br />Comparing polarization signatures in an image with those from simple scatterers is a simple way to...
                   Eigenvector Decomposition (Cloude)<br />Cloude showed that a general covariance matrix        can be de...
                   Eigenvector Decomposition (Cloude)<br />The eigenvectors for terrain with reflection symmetry are<br />
                    Eigenvector Decomposition (Cloude)<br />Note that<br />1<br />1<br />-1<br />-1<br />
Eigenvalue Images<br />
               Pauli Scattering Decomposition<br />
           Single vs Double Reflections<br />Dielectric Constant = 81<br />
                    Measures of Scattering Randomness<br />Entropy  (Cloude, Pottier..)<br />Radar Vegetation Index (van Z...
              Scatterer Randomness<br />These images convey the same information.  The details differ only because of<br /...
Scattering Mechanisms van Zyl 1989<br />
                   Alpha/Entropy Classification<br />Cloude and Pottier (1996) proposed the following description for the ...
                       Alpha/Entropy Classification<br />
Black Forest, Germany<br />
                  Eigenvector Decomposition<br />
         Model Based Decomposition<br />Model based algorithms decompose an observed covariance matrix in terms of known (...
        Model Based Decomposition<br />The eigenvalues of the following matrix must be zero or positive:<br />The maximum ...
          Example:  Freeman and Durden<br />
       Example:  Yamaguchi et al.<br />
               Non-Negative Eigenvalue Decomposition<br />The non-negative eigenvalue decomposition starts with a model fo...
                    Comparison with Freeman and Durden<br />
                    Comparison with Freeman and Durden<br />
                    Adaptive Model-Based Decomposition<br />The non-negative eigenvalue decomposition provides a simple wa...
Example<br />
                Arii et al. Adaptive Decomposition<br />Ariiet al. (2010) proposes a decomposition algorithm to analyze po...
Generalized Canopy Model<br />Arii, van Zyl and Kim, “A General Characterization for Polarimetric Scattering from Vegetati...
              Adaptive Decomposition Results             Mean Orientation Angle<br />
Azimuth Slopes<br />
             Adaptive Decomposition ResultsRandomness <br />
          Model-Based Decompositions<br />Model-based decompositions allow the analyst to inject human knowledge into the ...
Summary<br />Polarimetric radar images provide the opportunity to learn about the scattering mechanisms that dominate in e...
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TU1.L09.1 - APPLICATION OF POLARIMETRIC SAR TO EARTH REMOTE SENSING

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TU1.L09.1 - APPLICATION OF POLARIMETRIC SAR TO EARTH REMOTE SENSING

  1. 1. Application of Polarimetric SAR to Earth Remote Sensing<br />Jakob van Zyl and Yunjin Kim<br />Jet Propulsion Laboratory<br />California Institute of Technology<br />
  2. 2. Overview<br />Polarimetric SAR data are becoming more available, both in single pass and interferometric form<br />Because the full vector nature of the electromagnetic wave is preserved, theoretically one could perform a more complete analysis of scattering<br />There are many different ways to approach the analysis of a polarimetric data set.<br />New users are often overwhelmed and confused<br />It is vitally important that the polarimetric community provides simple guides on how to analyze data.<br />
  3. 3. Basic Tools: Polarization Signature<br />The polarization Signature is a simple graphical way to display the radar cross-section as a function of polarization. <br />Usually display co- and cross-polarization signatures<br />
  4. 4. Polarization Signatures A New Perspective<br />
  5. 5. Dihedral Corner Reflector<br />
  6. 6. Rotated Dihedral<br />
  7. 7. Three Orthogonal Scatterers<br />Trihedral Dihedral Rotated Dihedral<br />These are also the eigenvectors of the Pauli basis<br />
  8. 8. Effect of Phase Calibration Error<br />No Error<br />45 Degrees<br />90 Degrees<br />180 Degrees<br />135 Degrees<br />The signature is rotated about the S1 axis by half the phase calibration error value. Co-pol nulls are in the S2-S3 plane.<br />
  9. 9. Effect Of Co-Channel Imbalance<br />Signatures are distorted. Co-pol nulls are in the S1-S3 plane<br />
  10. 10. Dipole Orientation<br />Horizontal 45 Degrees Vertical<br />The angle of the co-pol maximum relative to the S1 axis is exactly twice the orientation angle of the dipole<br />
  11. 11. What do we Have Here?<br />
  12. 12. Polarization Synthesis<br />
  13. 13. Check Signatures<br />
  14. 14. Signature Analysis<br />Comparing polarization signatures in an image with those from simple scatterers is a simple way to infer what scattering mechanisms were present in an image<br />Checking signatures on a pixel by pixel basis is very tedious and unrealistic as an analysis tool<br />Our analysis techniques must be amenable to image processing<br />
  15. 15. Eigenvector Decomposition (Cloude)<br />Cloude showed that a general covariance matrix can be decomposed as follows:<br />Here, are the eigenvalues of the covariance matrix, are its eigenvectors, and means the adjoint (complex conjugate transposed) of .<br />In the monostatic (backscatter) case, the covariance matrix has one zero eigenvalue, and the decomposition results in at most three nonzero covariance matrices.<br />
  16. 16. Eigenvector Decomposition (Cloude)<br />The eigenvectors for terrain with reflection symmetry are<br />
  17. 17. Eigenvector Decomposition (Cloude)<br />Note that<br />1<br />1<br />-1<br />-1<br />
  18. 18. Eigenvalue Images<br />
  19. 19. Pauli Scattering Decomposition<br />
  20. 20. Single vs Double Reflections<br />Dielectric Constant = 81<br />
  21. 21. Measures of Scattering Randomness<br />Entropy (Cloude, Pottier..)<br />Radar Vegetation Index (van Zyl and Kim)<br />Pedestal Height (van Zyl, Durdenet al.)<br />
  22. 22. Scatterer Randomness<br />These images convey the same information. The details differ only because of<br />scaling and linearity.<br />
  23. 23. Scattering Mechanisms van Zyl 1989<br />
  24. 24. Alpha/Entropy Classification<br />Cloude and Pottier (1996) proposed the following description for the eigenvectors of the covariance matrix:<br />The average alpha angle is then calculated using<br />
  25. 25. Alpha/Entropy Classification<br />
  26. 26. Black Forest, Germany<br />
  27. 27. Eigenvector Decomposition<br />
  28. 28. Model Based Decomposition<br />Model based algorithms decompose an observed covariance matrix in terms of known (and expected) model derived covariance matrices.<br />All individual covariance matrices must satisfy some basic requirements<br />The observed scattering power for any polarization combination can never be negative<br />We can use this fact to determine the allowable values of a in the decomposition above<br />
  29. 29. Model Based Decomposition<br />The eigenvalues of the following matrix must be zero or positive:<br />The maximum value of a that can be used is that value that ensures non-negative eigenvalues for the matrix on the right.<br />
  30. 30. Example: Freeman and Durden<br />
  31. 31. Example: Yamaguchi et al.<br />
  32. 32. Non-Negative Eigenvalue Decomposition<br />The non-negative eigenvalue decomposition starts with a model for the canopy scattering and subtracts that from the observed covariance matrix<br />The remainder matrix is then further decomposed using an eigenvector decomposition<br />The first two eigenvectors are interpreted as odd and even numbers of reflections (single and double reflections)<br />van Zyl, Arii and Kim, “Model-Based Decomposition of Polarimetric SAR Covariance, Matrices Constrained for Non-Negative Eigenvalues” In Press, IEEE Trans. On Geosci and Remote Sens., 2010<br />
  33. 33. Comparison with Freeman and Durden<br />
  34. 34. Comparison with Freeman and Durden<br />
  35. 35. Adaptive Model-Based Decomposition<br />The non-negative eigenvalue decomposition provides a simple way to compare different models to find which is the best fit to the observation<br />Different models are compared by observing the total power left in the remainder matrix<br />The model that leaves the least power in the remainder matrix provides the best fit<br />
  36. 36. Example<br />
  37. 37. Arii et al. Adaptive Decomposition<br />Ariiet al. (2010) proposes a decomposition algorithm to analyze polarimetric images<br />The canopy scattering is described by a generalized canopy scattering model <br />The canopy is described in terms of a randomness parameter and a mean orientation angle<br />Arii, van Zyl and Kim, “Adaptive Model-Based Decomposition of Polarimetric <br />SAR Covariance Matrices,” In Press, IEEE Trans. On Geosci and Remote Sens., 2010<br />
  38. 38. Generalized Canopy Model<br />Arii, van Zyl and Kim, “A General Characterization for Polarimetric Scattering from Vegetation Canopies,” In Press, IEEE Trans. On Geosci and Remote Sens., 2010<br />
  39. 39. Adaptive Decomposition Results Mean Orientation Angle<br />
  40. 40. Azimuth Slopes<br />
  41. 41. Adaptive Decomposition ResultsRandomness <br />
  42. 42. Model-Based Decompositions<br />Model-based decompositions allow the analyst to inject human knowledge into the investigation<br />For this type of investigation to make sense, the models should be applicable to the image being analyzed<br />One may have to take terrain effects into account when performing the decomposition by first removing the effects of azimuth rotations<br />
  43. 43. Summary<br />Polarimetric radar images provide the opportunity to learn about the scattering mechanisms that dominate in each pixel.<br />Simple tools can provide a quick overview of the scattering present in an image.<br />Model-based decomposition is a simple way to identify the most appropriate model that best describes the observed scattering in each pixel<br />Once the most appropriate models are identified, further quantitative analysis can be performed.<br />

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