Lorentzian hard thresholding pursuit for compressed sensing in the presence of impulsive noise

The Lorentzian hard thresholding pursuit algorithm is proposed in this paper to achieve efficient reconstruction for compressed sensing in the presence of impulsive noise. In the Lorentzian hard thresholding pursuit algorithm, the minimum LL₂ norm problem is solved with respect to a support which is obtained through the hard thresholding operator. The convergence and reconstruction performance of the Lorentzian hard thresholding pursuit algorithm is proved in theory in this paper. Experimental results show that the reconstruction performance of the Lorentizian hard thresholding pursuit algorithm is superior to the Lorentzian iterative hard thresholding algorithm which is also an effective algorithm for sparse reconstruction of compressed sensing in the impulsive noise environment.