Texture and speckle statistics in polarimetric SAR synthesized images

We investigate in this paper the one-point statistical properties of the backscattered power derived by polarization synthesis of polarimetric synthetic aperture radar (SAR) observations. In particular, we focus our attention on the normalized second moment of intensity and its dependency on the polarization state. For the analysis of this dependency, a novel graphical representation - an extension of the polarization response - is introduced: the polarimetric texture signature. The second moment of backscattered power characterizes statistically the variation of the radar signal due to speckle and the underlying radar cross section. The classical texture product model with a scalar radar reflectivity implies that the normalized second moment of intensity does not depend on the polarization state. However, such dependency is found in experimental observations, a fact that calls for further investigation of the phenomenon. Considering at first speckle statistics for homogeneous areas having no texture, it is demonstrated that correlation among the single-look speckle patterns, which are added on an intensity basis in a multilook operation, is responsible for a weak polarization dependency of the normalized second moment. Concerning the textural properties, a new model is proposed - the mixture model - where it is assumed that polarimetrically diverse scattering mechanisms contribute to the total return from an ensemble of resolution elements. Numerical simulations are used to reconstruct the texture signatures according to the mixture model, starting from simple assumptions related to scattering processes from natural targets. It is found that the polarimetric texture signature can be an interesting discriminator of weak targets against clutter, when only polarimetric diversity and not radiometric diversity plays a role. The effects predicted by the theory are confirmed by experimental analysis of polarimetric data acquired by the Jet Propulsion Laboratory AIRSAR sensor. Finally a classification scheme based on the polarimetric texture signature is proposed.