Breaking the ?_1 Recovery Thresholds with Reweighted ?_1 Optimization

摘要

It is now well understood that ?_1 minimization algorithm is able to recover sparse signals from incomplete measurements [2], [1], [3] and sharp recoverable sparsity thresholds have also been obtained for the ?_1 minimization algorithm. In this paper, we investigate a new iterative reweighted ?_1 minimization algorithm and showed that the new algorithm can increase the sparsity recovery threshold of ?_1 minimization when decoding signals from relevant distributions. Interestingly, we observed that the recovery threshold performance of the new algorithm depends on the behavior, more specifically the derivatives, of the signal amplitude probability distribution at the origin.