Block-sparsity: Coherence and efficient recovery

Authors:
Yonina C. Eldar;Helmut Bolcskei
Affiliations:
Technion, Haifa, Israel;ETH Zurich, Switzerland
Venue:
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Year:
2009

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Abstract

We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occurring in clusters. Based on an uncertainty relation for block-sparse signals, we define a block-coherence measure and 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-sparsity is shown to guarantee successful recovery through a mixed ℓ2/ℓ1 optimization approach. The significance of the results lies in the fact that making explicit use of block-sparsity can yield better reconstruction properties than treating the signal as being sparse in the conventional sense, thereby ignoring the additional structure in the problem.