Hard Thresholding based Robust Algorithm for Multiple Measurement Vectors

In this paper, we present Simultaneous Lorentzian Iterative Hard Thresholding (SLIHT) algorithm for recovering complex valued, jointly sparse signals corrupted by heavy tailed noise in the multiple measurement vector model in compressed sensing. The proposed algorithm uses Lorentzian norm as the underlying cost function which provides robustness against heavy tailed noise, e.g., impulsive noise. Analysis is carried out for the proposed algorithm using Majorization-Minimization framework and we show that under proper selection of parameters, the proposed SLIHT algorithm produces a sequence of row sparse estimates for which the Lorentzian norm of the residual is non-increasing. Extensive simulation studies are carried out against state of the art methods and it is observed that performance of the proposed algorithm is better or at least at par with the current methods.