Non-Gaussian mixture models for detection and estimation in heavy-tailed noise

Scale mixtures of the Gaussian have been used to approximate the PDF of symmetric alpha stable processes. Such mixtures, however, cannot easily capture the heavy-tails. We propose to use Cauchy-Gaussian mixtures which are natural in this setting. Variations of standard EM algorithms can be used to estimate the parameters of the noise PDFs under various scenarios (noise-only data, weak-signal assumption, partially known-signal case). The fitted mixture models can be used for detection and estimation. In the multivariate case, we present several results on Gaussian mixture approximations of sub-Gaussian PDFs, including robust estimation of the underlying correlation matrix.