Noisy Signal Recovery via Iterative Reweighted L1-Minimization

Compressed sensing has shown that it is possible to reconstruct sparse high dimensional signals from few linear measurements. In many cases, the solution can be obtained by solving an L1-minimization problem, and this method is accurate even in the presence of noise. Recent a modified version of this method, reweighted L1-minimization, has been suggested. Although no provable results have yet been attained, empirical studies have suggested the reweighted version outperforms the standard method. Here we analyze the reweighted L1-minimization method in the noisy case, and provide provable results showing an improvement in the error bound over the standard bounds.