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 components. This drives traditional linear operators to failure, since gross observation errors are spread uniformly over generated compressed measurements, whilst masking critical information content of observed signal. To address problem, paper exploits power symmetric alpha-stable (S?S) distributions design a robust nonlinear operator capable suppressing effects additive noise. Specifically, generalized matched filter introduced generating measurements fashion, which achieves increased robustness noise, thus subsequently improving accuracy sparse reconstruction algorithms. emerges naturally case modeled by S?S distributions, as an effective mechanism downweighting outliers noisy The theoretical justification along with experimental evaluation demonstrate improved performance our CS framework compared against state-of-the-art techniques broad range environments.