Statistical Tests for Symmetries in Polarimetric Scattering Coherency Matrices

The second-order statistics are among the most important observables in synthetic aperture radar (SAR) polarimetry and are usually reported as covariance or coherence matrices. They are restricted to particular forms provided the target exhibits a certain kind of symmetry. As these constraints are not exactly fulfilled in real data, statistical tests are proposed for checking the validity of an invariance hypothesis. The application of these likelihood-ratio tests to airborne L-band data reveals a strong dependence of the test statistics on both the land cover and the number of looks; furthermore, temporal changes such as vegetation growth are evident: for example, lack of reflection symmetry for mature rape fields. This finding is at odds with commonly employed models, which assume (and predict) reflection invariance. For the Freeman-Durden decomposition, which relies on reflection symmetry, the connection between this invariance and negative powers (unphysical result) is found to be weak.