Improved Block-Sparse Recovery Bound Using Cumulative Block Coherence

Pouria Saidi, George K. Atia, Azadeh Vosoughi

Abstract: Block coherence extends the conventional notion of coherence to capture the interdependence of blocks in a given dictionary. This measure is the basis for various recovery bounds of block-sparse signals, i.e., signals with clustered support, from under-determined systems of equations. In this paper, we extend the block coherence measure by introducing the notion of cumulative block coherence, which measures the maximum coherence between a block and a collection of other blocks. We show analytically that the cumulative block coherence yields relaxed sufficient conditions on the sparsity level for exact recovery of a block-sparse signal.