A perturbation analysis of nonconvex block-sparse compressed sensing

This paper proposes a completely perturbed mixed ℓ2/ℓp 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 ℓ2/ℓp 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 δ2K < 1 [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.