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$\mathcal {G}_{0}$, generalized gamma, and the lognormal distribution. The numerical analysis demonstrates the superior performance and flexibility of the proposed distribution for modeling urban scenes.

Synthetic aperture radar (SAR) and ultrasound (US) are two important active imaging techniques for remote sensing, both of which are subject to speckle noise caused by coherent summation of back-scattered waves and subsequent nonlinear envelope transformations. Estimating the characteristics of this multiplicative noise is crucial to develop denoising methods and to improve statistical inference from remote sensing images. In this paper, reversible jump Markov chain Monte Carlo (RJMCMC) algorithm has been used with a wider interpretation and a recently proposed RJMCMC-based Bayesian approach, trans-space RJMCMC, has been utilized. The proposed method provides an automatic model class selection mechanism for remote sensing images of SAR and US where the model class space consists of popular envelope distribution families. The proposed method estimates the correct distribution family, as well as the shape and the scale parameters, avoiding performing an exhaustive search. For the experimental analysis, different SAR images of urban, forest and agricultural scenes, and two different US images of a human heart have been used. Simulation results show the efficiency of the proposed method in finding statistical models for speckle.