Spherical Symmetry of Complex Stochastic Models in Multivariate High-Resolution PolSAR Images

The multiplicative model, expressed as a product between the square root of a scalar positive quantity (texture) and the description of an equivalent homogeneous surface (speckle), is one of the most appropriate and disseminated models used to describe high-resolution polarimetric synthetic aperture radar (PolSAR) clutter. Generally, the texture is assumed polarization independent, which causes PolSAR data to present a spherical symmetry property, allowing for the usage of most of the algorithms present in the literature. Nevertheless, the existence of polarization-dependent clutter has also been reported, for which specific algorithms need to be derived. Therefore, it becomes clear that the first step in SAR data analysis should be the validation of the model employed. Within this context, this paper presents a new methodological framework to assess the conformity of multivariate high-resolution SAR data with respect to the product model in terms of asymptotic statistics. More precisely, spherical symmetry is investigated by applying statistical hypothesis testing on the structure of the quadricovariance matrix. Simulated data, data from the P-band airborne data set acquired by the Office National d'Études et de Recherches Aérospatiales (ONERA) over the French Guiana in 2009 in the frame of the European Space Agency campaign TropiSAR and a RAMSES X-band image acquired over Brétigny, France, are taken into consideration to investigate the performance of the derived test. The detection results are qualitatively and quantitatively analyzed, and some important conclusions are drawn regarding the methodology employed in analyzing SAR data.