Robust Sparse Signal Recovery in the Presence of the S \alphaS Noise

In this letter, robust sparse signal recovery is considered in the presence of the symmetric α-stable distributed noise. An M-estimate type model is constructed by approximating the location score function of the noise. A reweighed iterative hard thresholding algorithm is proposed to recover the sparse signal. The basis functions for the approximation and the recovery performance of the proposed algorithm are discussed. Simulations are given to demonstrate the validity of our results.