Non-Gaussian Multivariate Probability Models and Parameter Estimation For Polarimetric Synthetic Aperture Radar Data.

The inadequacy of gaussian statistics in describing certain regions of a synthetic aperture radar (SAR) image can be explained by the violation of fundamental gaussian assumptions due to the increase in spatial resolution and target heterogeneity. Many non-gaussian probability models, competing in modeling flexibility, mathematical tractability, and simplicity/accuracy of parameter estimation, have been proposed in the last two decades to model single-channel and polarimetric SAR (PolSAR) data. This thesis explores the flexible polarimetric Q distribution, which has many other non-gaussian probability models as its special forms. Previously, it has not been applied to PolSAR data primarily because of its relatively complicated probability density function (pdf). But recently, other flexible distributions, e. g. Kummer-U distribution, with similarly complicated pdfs have been successfully applied to PolSAR data. Therefore, it is expected that the application of Q distribution, along with the proposal of its new, accurate, and efficient parameter estimators, to model PolSAR data will bring significant contributions to the field. Firstly, singlelook version of polarimetric Q distribution is derived. Then, several new parameter estimators for this distribution are proposed. The performance of these estimators are compared to each other on simulated PolSAR data. One of the better performing estimators results from the novel analysis of Q distribution using Mellin kind statistics. However, this estimator does not have closed form expressions, which is an undesirable property. A new framework for parameter estimation, based on fractional moments of multilook polarimetric whitening filter, is thus proposed. It results in simple, accurate, and computationally inexpensive estimators for all the well known non-gaussian probability models including the Q distribution. On real PolSAR data, the fitting accuracy of Q distribution, bundled with its new estimators, is compared with some other competitive non-gaussian models. It is found that the proposed distribution adequately fits PolSAR data significantly better than its special cases, and very similar to the Kummer-U distribution. However, the software implementation of Q distribution pdf is observed to be relatively more stable than the Kummer-U distribution pdf