The compound truncated Poisson Cauchy model: A descriptor for multimodal data

Abstract

Multimodal data are often present in synthetic aperture radar (SAR) image processing. Such images are often modeled by probability mixtures, but such solution may involve a large number of parameters and its inference becomes challenging. To address this issue, we proposed a probability distribution capable of describing multimodal data with only three parameters. The introduced model is defined by the sum of a random number, following the truncated Poisson law, of independent random variables with the Cauchy model, called compound truncated Poisson Cauchy (CTPC) distribution. We derived the characteristic function (cf), a distance measure between cfs, and provided estimators for the CTPC parameters: maximum likelihood estimators (MLEs) and quadratic distance estimators (QDEs). Furthermore, we derived a goodness-of-fit (GoF) distance based on the CTPC law and its empirical cf. To quantify the performance of the proposed estimators and GoF statistic, we employed a Monte Carlo simulation and the results suggest that QDEs outperform MLEs. Finally, we detail a numerical experiment with actual SAR data which describes a segment of SAR intensities with at least two types of textures. Our model could outperform six SAR intensities models: Weibull, gamma, generalized gamma, K, G0, and beta generalized normal.