Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 58, Issue 6, Pages 3042-3054Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2010.2044837
Keywords
Basis pursuit; block-sparsity; compressed sensing; matching pursuit
Categories
Funding
- European Commission
- Israel Science Foundation [1081/07]
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We consider efficient methods for the recovery of block-sparse signals-i.e., sparse signals that have nonzero entries occurring in clusters-from an underdetermined system of linear equations. An uncertainty relation for block-sparse signals is derived, based on a block-coherence measure, which we introduce. We then show that a block-version of the orthogonal matching pursuit algorithm recovers block k-sparse signals in no more than k steps if the block-coherence is sufficiently small. The same condition on block-coherence is shown to guarantee successful recovery through a mixed l(2)/l(1)-optimization approach. This complements previous recovery results for the block-sparse case which relied on small block-restricted isometry constants. The significance of the results presented in this paper lies in the fact that making explicit use of block-sparsity can provably yield better reconstruction properties than treating the signal as being sparse in the conventional sense, thereby ignoring the additional structure in the problem.
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