A perturbation analysis of nonconvex block-sparse compressed sensing

Abstract This paper proposes a completely perturbed mixed l 2 /l p minimization to deal with a model of completely perturbed block-sparse compressed sensing. Based on the block restricted isometry property (BRIP), the paper extends the study to a complete perturbation model which considers not only noise but also perturbation, establishes a sufficient condition for efficiently recovering the block-sparse signal under the complete perturbation case, and offers eventually a superior approximation precision. The precision, in this paper, can be characterized in terms of the total noise and the best K -term approximation. The adopted mixed l 2 /l p minimization also gains better robustness and stability than ever that on recovering the block-sparse signal with the presence of total noise. Especially, the analysis of this study shows the condition is the best sufficient condition δ 2 K [20] when p tends to zero and a  > 1 for the complete perturbation and block-sparse signal. The numerical experiments carried out confirm excellently the assessed performance.

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