Polarimetric scattering indexes and information entropy of the SAR imagery for surface monitoring

The Mueller matrix solution and eigen-analysis of the coherency matrix for completely polarimetric scattering have been applied to analysis of the SAR (synthetic aperture radar) imagery. Co-polarized and cross-polarized backscattering for any polarized incidence can be obtained. The polarization index is usually defined as a parameter to classify the difference between polarized scattering signatures from the terrain surfaces. In this paper, the eigen-values of the coherency matrix and information entropy are derived to directly relate with measurements of the co-polarized and cross-polarized indexes. Thus, it combines the Mueller matrix simulation, the information entropy of the coherence matrix, and two polarization indexes together and yields a quantitative evaluation for surface classification in the SAR imagery. This theory is applied to analysis of the AirSAR images and fields measurements.