An Approximate Representation of Heavy-tailed Noise:Bi-parameter Cauchy-Gaussian Mixture Model

摘要

As a non-Gaussian statistic model,alpha stable distribution has gained much attention due to its generality to represent heavy-tailed and impulsive interference.Unfortunately,there is no closed form expression for the probability density function of alpha-stable distributions.Hereby,finding the approximate expressions is of importance for signal detection and denoising.In this paper,we present a novel approximate expression,which is a simplified version of Cauchy-Gaussian mixture (CGM) for symmetric α-stable (SαS) distribution,called Bi-parameter CGM (BCGM).Such a model has a complete closed-form expression,and hence is more tractable than classical GMM and CGM.