Application of Mellin-Kind Statistics to Polarimetric ${\cal G}$ Distribution for SAR Data

The K distribution can be arguably regarded as one of 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 distribution filled some deficiencies left unaccounted by the K model. The G model actually resulted as a special case of a more general model; the G distribution, which also has the K model as its special form. Singlelook complex (SC) and multilook complex (MC) 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 Method of Log Cumulants (MoLC), and Method of Matrix Log Cumulants (MoMLC). These estimators show superior performance characteristics for product model distributions like the G model. Diverse regions in TerraSAR-X polarimetric SAR (PolSAR) data have also been statistically analyzed using the G model with its new and old estimators. Formal Goodness-of-fit (GoF) testing, based on MKS theory, has been used to assess the fitting accuracy between different estimators and also between G, K, G, and Kummer-U models.