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| In this paper, the stable recovery of block sparse signals is investigated.A general mixed $l_{p}/l_{q}$ optimization algorithm is proposed, under which the block restricted isometry property (block RIP) and the block null space property (block NSP) are both shown to be sufficient conditions on a measurement matrix for stable recovery of block-sparse signals. Moreover, a new concept of the block sparse approximationproperty (block SAP) is defined in this paper. It is shown that the block SAP is also a sufficient condition on a measurement matrix for stably recovering block-sparse signals based on the mixed $l_{p}/l_{q}$ optimization algorithm. Finally, the relationship between the block SAP, the block RIP, and the block NSP are studied. |
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| Keywords:Approximation theory, compressed sensing, Block-sparse signal, Mixed optimization. |
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