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Application of Polarimetric SAR to Earth Remote Sensing Jakob van Zyl and Yunjin Kim Jet Propulsion Laboratory California Institute of Technology
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.
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
Three Orthogonal Scatterers Trihedral Dihedral Rotated Dihedral These are also the eigenvectors of the Pauli basis
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.
Effect Of Co-Channel Imbalance Signatures are distorted. Co-pol nulls are in the S1-S3 plane
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
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
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.
Eigenvector Decomposition (Cloude) The eigenvectors for terrain with reflection symmetry are
Eigenvector Decomposition (Cloude) Note that 1 1 -1 -1
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
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.
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
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
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
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
Adaptive Decomposition Results Mean Orientation Angle
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
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.