Breaking the ℓ_1 recovery thresholds with reweighted ℓ_1 optimization

It is now well understood that ℓ_1 minimization algorithm is able to recover sparse signals from incomplete measurements and sharp recoverable sparsity thresholds have also been obtained for the l1 minimization algorithm. In this paper, we investigate a new iterative reweighted ℓ_1 minimization algorithm and showed that the new algorithm can increase the sparsity recovery threshold of ℓ_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