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Recovery of Block-Sparse Representations from Noisy Observations via Orthogonal Matching Pursuit

We study the problem of recovering the sparsity pattern of block-sparse signals from noise-corrupted measurements. A simple, efficient recovery method, namely, a block-version of the orthogonal matching pursuit (OMP) method, is considered in this paper and its behavior for recovering the block-sparsity pattern is analyzed. We provide sufficient conditions under which the block-version of the OMP can successfully recover the block-sparse representations in the presence of noise. Our analysis reveals that exploiting block-sparsity can improve the recovery ability and lead to a guaranteed recovery for a higher sparsity level. Numerical results are presented to corroborate our theoretical claim.

preprint2011arXivOpen access
Jun FangHongbin Li
math.ITInformation Theory
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Jun FangHongbin Li

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