Robust nonlinear compressive sampling using symmetric alpha-stable distributions

Conventional compressive sampling (CS) primarily assumes light-tailed models for the underlying signal and/or noise statistics. Nevertheless, this assumption is abolished when operating in impulsive environments, where non-Gaussian infinite-variance processes arise for the signal and/or noise components. This drives traditional linear sampling operators to failure, since the gross observation errors are spread uniformly over the generated compressed measurements, whilst masking the critical information content of the observed signal. To address this problem, this paper exploits the power of symmetric alpha-stable (S alpha S) distributions to design a robust nonlinear compressive sampling operator capable of suppressing the effects of infinite-variance additive observation noise. Specifically, a generalized alpha-stable matched filter is introduced for generating compressed measurements in a nonlinear fashion, which achieves increased robustness to impulsive observation noise, thus subsequently improving the accuracy of traditional sparse reconstruction algorithms. This filter emerges naturally in the case of additive observation noise modeled by S alpha S distributions, as an effective mechanism for downweighting gross outliers in the noisy signal. The theoretical justification along with the experimental evaluation demonstrate the improved performance of our nonlinear CS framework when compared against state-of-the-art CS techniques for a broad range of impulsive environments. (C) 2020 Elsevier B.V. All rights reserved.