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.
© 2009 Signals, Systems and Computers
Needell, D., "Noisy signal recovery via iterative reweighted L1-minimization", Proc. Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA Nov. 2009. doi: 10.1109/ACSSC.2009.5470154