Block-sparse signals: uncertainty relations and efficient recovery

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 `2=`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 th...

• Type: Journal
• Year: 2010
• Where: TSP
• Authors: Yonina C. Eldar, Patrick Kuppinger, Helmut Bölcskei
• Keywords: Artificial Intelligence, Block K-sparse Signals, Block-sparse Signals, Orthogonal Matching Pursuit, TSP 2010