Sparse Recovery With Block Multiple Measurement Vectors Algorithm

This paper investigates the performance of the block multiple measurement vectors (BMMV) algorithm in reconstructing block joint sparse matrices. We prove that if 41) obeys block restricted isometry property with 8 K+1 <; Nf +1 , then BMMV perfectly reconstructs any block K -joint sparse matrix X from observations Y = (DX in K iterations. We also show that BMMV may not reconstruct block K -joint sparse matrices in K iterations under the condition K+1 > , 1 That is to say, the condition 8K +l <; , 1 is v1C+1 vIC+1 optimal for the BMMV algorithm.