  In this paper, we present a novel statistical model, $\textit{the
generalized-Gaussian-Rician}$ (GG-Rician) distribution, for the
characterization of synthetic aperture radar (SAR) images. Since accurate
statistical models lead to better results in applications such as target
tracking, classification, or despeckling, characterizing SAR images of various
scenes including urban, sea surface, or agricultural, is essential. The
proposed statistical model is based on the Rician distribution to model the
amplitude of a complex SAR signal, the in-phase and quadrature components of
which are assumed to be generalized-Gaussian distributed. The proposed
amplitude GG-Rician model is further extended to cover the intensity SAR
signals. In the experimental analysis, the GG-Rician model is investigated for
amplitude and intensity SAR images of various frequency bands and scenes in
comparison to state-of-the-art statistical models that include $\mathcal{K}$,
Weibull, Gamma, and Lognormal. In order to decide on the most suitable model,
statistical significance analysis via Kullback-Leibler divergence and
Kolmogorov-Smirnov statistics are performed. The results demonstrate the
superior performance and flexibility of the proposed model for all frequency
bands and scenes and its applicability on both amplitude and intensity SAR
images. The Matlab package is available at
https://github.com/oktaykarakus/GG-Rician-SAR-Image-Modelling.
