A note on block-sparse signal recovery with coherent tight frames

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 frame D. By introducing the notion of block D -restricted isometry property (D -RIP), we establish several sufficient conditions for the proposed mixed l 2 / l 1 -analysis method to guarantee stable recovery of nearly block-sparse signals in terms of D. One of the main results of this note shows that if the measurement matrix satisfies the block D -RIP with constants δ k < 0.307, then the signals which are nearly block k -sparse in terms of D can be stably recovered via mixed l 2 / l 1 -analysis in the presence of noise.