The Perturbation Analysis of Nonconvex Low-Rank Matrix Robust Recovery

Article; Early Access

关键词: NUCLEAR NORM MINIMIZATION;    SPARSE SIGNAL RECOVERY;    P-ISOMETRY PROPERTIES;    STABLE RECOVERY;    COMPLETION;   

DOI  :  10.1109/TNNLS.2023.3289209

来源: SCIE

【 摘 要 】

In this article, we bring forward a completely perturbed nonconvex Schatten p-minimization to address a model of completely perturbed low-rank matrix recovery (LRMR). This article based on the restricted isometry property (RIP) and the Schatten-p null space property (NSP) generalizes the investigation to a complete perturbation model thinking over not only noise but also perturbation, and it gives the RIP condition and the Schatten-p NSP assumption that guarantee the recovery of low-rank matrix and the corresponding reconstruction error bounds. In particular, the analysis of the result reveals that in the case that p decreases 0 and a > 1 for the complete perturbation and low-rank matrix, the condition is the optimal sufficient condition d(2r )< 1 (Recht et al., 2010). In addition, we study the connection between RIP and Schatten-p NSP and discern that Schatten-p NSP can be inferred from the RIP. The numerical experiments are conducted to show better performance and provide outperformance of the nonconvex Schatten p-minimization method comparing with the convex nuclear norm minimization approach in the completely perturbed scenario.

【 授权许可】

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