Lorentzian based iterative hard thresholding for compressed sensing

In this paper we propose a robust iterative hard thresholding (IHT) algorithm for reconstructing sparse signals in the presence of impulsive noise. To address this problem, we use a Lorentzian cost function instead of the L2 cost function employed by the traditional IHT algorithm. The derived algorithm is comparable in computational load to the least squares based IHT. Analysis of the proposed method demonstrates its robustness under heavy-tailed models. Simulations show that the proposed algorithm significantly outperform commonly employed sparse reconstruction techniques in impulsive environments, while providing comparable reconstruction quality in less demanding, light-tailed environments.