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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 Â¿1-minimization problem, and this method is accurate even in the presence of noise. Recently a modified version of this method, reweighted Â¿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 Â¿1-minimization method in the noisy case, and provide provable results showing an improvement in the error bound over the standard bounds.
Date of Conference: 1-4 Nov. 2009