Stokes matrix eigenvectors of fully polarimetric SAR data

Abstract

The Stokes matrices of about 1 billion pixels of fully polarimetric single look and multilook SIR-C L-band data were analyzed. The Stokes matrix is a 4x4 real symmetric matrix. The Jacobi eigenvalue algorithm was used to determine the eigenvalues and eigenvectors of each matrix. A remarkable result is that all 1 billion pixels did not have more than one eigenvector which satisfied the Stokes vector property where ∥S 0 ∥ 2 ≥ ∥S 1 ∥ 2 + ∥S 2 ∥ 2 + ∥S 3 ∥ 2 and So > 0. Less than 1 percent of the pixels had no eigenvectors which satisfied this property. The equality condition corresponds to cases where the eigenvector describes a fully polarized Stokes vector. Images were generated from the fraction of the polarized part and unpolarized part of these Stokes vectors, the sine of the ellipticity as well as the eigenvalue. Images were generated as well from the phase statistics generated from the Mueller scattering matrix. These images strongly correlate with the span imagery. The reported resolution for the multilook SIR-C data is 25 m. Each resolution cell is populated by a large number of scattering centers at this relatively low resolution. RADARSAT-2, which was launched on Dec 14, 2007, is capable of much higher resolution fully polarimetric data. Application of this type of analysis to such data will allow consideration of the signatures of the more dominant scatterers in a resolution cell.