Application of Mellin-Kind Statistics to Polarimetric <inline-formula> <tex-math notation="TeX">${\cal G}$</tex-math></inline-formula> Distribution for SAR Data

Abstract

The K distribution can arguably be regarded as one of the most successful and widely used models for radar data. However, in the last two decades, we have seen tremendous growth in even more accurate modeling of radar statistics. In this regard, the relatively recent G <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sup> distribution has filled some deficiencies that were left unaccounted for by the K model. The G <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sup> model, in fact, resulted as a special case of a more general model, the G distribution, which also has the K model as its special form. Single-look and multilook complex polarimetric extensions of these models (and many others) have also been proposed in this prolific era. Unfortunately, statistical analysis using the polarimetric G distribution remained limited, primarily because of more complicated parameter estimation. In this paper, the authors have analyzed the G model for its parameter estimation using state-of-the-art univariate and matrix-variate Mellin-kind statistics (MKS). The outcome is a class of estimators based on the method of log cumulants and the method of matrix log cumulants. These estimators show superior performance characteristics for product model distributions such as the G model. Diverse regions in TerraSAR-X polarimetric synthetic aperture radar data have also been statistically analyzed using the G model with its new and old estimators. Formal goodness-of-fit testing, based on the MKS theory, has been used to assess the fitting accuracy between different estimators and also between the G, K, G <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sup> , and Kummer- U models.