NDLI: Block-Sparse Signals: Uncertainty Relations and Efficient Recovery

Content Provider	IEEE Xplore Digital Library
Author	Eldar, Y.C. Kuppinger, P. Bolcskei, H.
Copyright Year	1991
Abstract	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 -sparse signals in no more than steps if the block-coherence is sufficiently small. The same condition on block-coherence is shown to guarantee successful recovery through a mixed -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.
Sponsorship	IEEE Signal Processing Society
Starting Page	3042
Ending Page	3054
Page Count	13
File Size	553546
File Format	PDF
ISSN	1053587X
Volume Number	58
Issue Number	6
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-06-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Uncertainty Matching pursuit algorithms Pursuit algorithms Equations Clustering algorithms Compressed sensing Vectors Sparse matrices Wireless communication matching pursuit Basis pursuit block-sparsity compressed sensing
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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