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Sparse Recovery With Block Multiple Measurement Vectors Algorithm
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DOI：10.1109/ACCESS.2019.2891568.png)
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Abstract
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This paper investigates the performance of the block multiple measurement vectors (BMMV) algorithm in reconstructing block joint sparse matrices. We prove that if Phi obeys block restricted isometry property with delta(K)(+1) < 1/root K+1, then BMMV perfectly reconstructs any block K-joint sparse matrix X from observations Y = Phi X in K iterations. We also show that BMMV may not reconstruct block K-joint sparse matrices in K iterations under the condition delta(K)(+1) >= 1/root K+1. That is to say, the condition delta(K)(+1) < 1/root K+1 is optimal for the BMMV algorithm.
Keywords:
Sparse recovery
block restricted isometry property
block multiple measurement vectors (BMMV) algorithm
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