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Mathematics > Numerical Analysis

arXiv:0904.3780 (math)
[Submitted on 24 Apr 2009]

Title:Noisy Signal Recovery via Iterative Reweighted L1-Minimization

Authors:Deanna Needell
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Abstract: 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.
Subjects: Numerical Analysis (math.NA); Information Theory (cs.IT)
Cite as: arXiv:0904.3780 [math.NA]
  (or arXiv:0904.3780v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.0904.3780

Submission history

From: Deanna Needell [view email]
[v1] Fri, 24 Apr 2009 02:52:26 UTC (27 KB)
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