The Essence of Scattering Purity and Complexity in Radar Polarimetry

In this work, we propose two parameters in radar polarimetry: (i) scattering purity and (ii) scattering complexity. To obtain these expressions, we use inequalities on the bounds of the condition number in terms of the mean (m) and standard deviation (s) of the eigenvalues of a Hermitian positive semi-definite matrix. The polarimetric scattering purity characterizes the overall polarization structure in the scattered wave. In contrast, the polarimetric scattering complexity describes the mixture of orthogonal polarized pure components in the scattered wave. We discuss the variability of these metrics over various land cover classes using full-polarimetric C-band Synthetic Aperture Radar (SAR) data. We compare their spatial variations over the ocean surface, built-up areas, and vegetation. We notice significant differences in the purity and complexity characteristics across a wide range of targets in the scene.