Robust sampling and reconstruction methods for compressed sensing

Recent results in compressed sensing show that a sparse or compressible signal can be reconstructed from a few incoherent measurements. Compressive sensing systems are not immune to noise, which is always present in practical acquisition systems. In this paper we propose robust methods for sampling and reconstructing sparse signals in the presence of impulsive noise. Analysis of the proposed methods demonstrates their robustness under heavy-tailed models. Simulations show that the proposed methods outperform existing compressed sensing techniques in impulsive environments, while having similar performance in light-tailed environments.