This note discusses the recovery of signals from undersampled data in the situation that such signals are nearly block sparse in terms of an overcomplete and coherent tight frameD. By introducing the notion of blockD-restricted isometry property (D-RIP), we establish several sufficient conditions for the proposed mixedl2/l1-analysis method to guarantee stable recovery of nearly block-sparse signals in terms ofD. One of the main results of this note shows that if the measurement matrix satisfies the blockD-RIP with constantsδk<0.307, then the signals which are nearly blockk-sparse in terms ofDcan be stably recovered via mixedl2/l1-analysis in the presence of noise.
A Note on Block-Sparse Signal Recovery with Coherent Tight Frames