Cauchy–Rician Model for Backscattering in Urban SAR Images

Abstract

This letter presents a new statistical model for urban scene synthetic aperture radar (SAR) images by combining the Cauchy distribution, which is heavy tailed, with the Rician backscattering. The literature spans various well-known models most of which are derived under the assumption that the scene consists of multitudes of random reflectors. This idea specifically fails for urban scenes since they accommodate a heterogeneous collection of strong scatterers such as buildings, cars, and wall corners. Moreover, when it comes to analyzing their statistical behavior, due to these strong reflectors, urban scenes include a high number of high amplitude samples, which implies that urban scenes are mostly heavy-tailed. The proposed Cauchy–Rician model contributes to the literature by leveraging nonzero location (Rician) heavy-tailed (Cauchy) signal components. In the experimental analysis, the Cauchy–Rician model is investigated in comparison to state-of-the-art statistical models that include <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {G}_{0}$ </tex-math></inline-formula> , generalized gamma, and the lognormal distribution. The numerical analysis demonstrates the superior performance and flexibility of the proposed distribution for modeling urban scenes.