Texture and speckle statistics in polarimetric SAR synthesized images

A study on the texture and speckle statistics in polarimetric SAR synthesized images was carried out by the authors and presented in preliminary form at the IGARSS'95 Symposium. In this paper some results, which have been recently consolidated, are summarized. We introduce at first a formalism to measure from experimental SAR data and represent graphically and in concise form the dependency of the statistical properties of the image on the polarization state. In particular we focus our attention on the one point statistics and on the second order normalized moment dependency on the polarization state. This is an extension of the classical polarimetric signature, and in the case of the second order moment is called the polarimetric texture signature. Application of this formalism to a data set acquired by the NASA JPL AIRSAR polarimetric radar over the Le Landes forest reveals some distinct and interesting trends in the texture signatures. Theoretical explanation of the phenomenon starts from the consideration of the influence of the synthesis operation, seen as a linear transformation of random variables, on the probability distribution function of the radar signal. A first mechanism that underpins the second moment variation with polarization is defined; this effect arises when multi-look polarimetric data are derived in the space domain from correlated single look data, and is entirely due to the fading statistics. A second mechanism is postulated to account for the observed texture signatures, which is due to the polarimetric diversity of the underlying radar reflectivity. This asymmetry in the response of the scatterer to the polarized wave can be best modelled using a so called polarimetric mixture approach, whereby polarimetrically different scattering mechanisms are combined for each resolution cell. A Monte Carlo simulation approach is used to reconstruct the observed signatures, starting from the assumption of simple physical situations, which can be realizable in scattering processes from natural targets. An example is presented, related to a mixture of deterministic point targets and a vegetation clutter. An interesting consequence from the application point of view is that the polarimetric texture signature is found to be a discriminator of weak targets against a clutter, when only polarimetric diversity and not radiometric diversity plays a role.