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 ¿₁-minimization problem, and this method is accurate even in the presence of noise. Recently a modified version of this method, reweighted ¿₁-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 ¿₁-minimization method in the noisy case, and provide provable results showing an improvement in the error bound over the standard bounds.