The Polarimetric G Distribution for SAR Data Analysis

Remote sensing data, and radar data in particular, have become an essential tool for enviromental studies. Many airborne polarimetric sensors are currently operational, and many more will be available in the near future including spaceborne platforms. The signal-to-noise ratio of this kind of imagery is lower than that of optical information requiring, thus, a careful statistical modelling. This modelling may lead to useful or useless techniques for image processing and analysis, according to the agreement between the data and their assumed properties. Several distributions have been used to describe Synthetic Aperture Radar (SAR) data. Many of these univaritate laws arise by assuming the multiplicative model, such as Rayleigh, Square Root of Gamma, Exponential, Gamma, and the class of the KI distributions. The adequacy of these distributions depends on the detection (amplitude, intensity, complex etc.), the number of looks, and the homogeneity of the data. In Frery, Müller, Yanasse and Sant’Anna (1997) another class of univariate distributions, called G, was proposed to model extremely heterogeneous clutter, such as urban areas, as well as other types of clutter. This paper extends the univariate G family to the multivariate multilook polarimetric situation: the GP law. The new family has the classical polarimetric multilook KP distribution as a particular case, but another special case is shown more flexible and tractable, while having the same number of parameters and fully retaining their interpretability: the G0 P law. The main properties of this new multivariate distribution are shown. Some results of modelling polarimetric data using the G0 P distribution are presented for two airborne polarimetric systems and a variety of targets, showing its expresiveness beyond classical models.