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