TITLE:
A Perturbation Analysis of Low-Rank Matrix Recovery by Schatten p-Minimization
AUTHORS:
Zhaoying Sun, Huimin Wang, Zhihui Zhu
KEYWORDS:
Nonconvex Schatten p-Norm, Low-Rank Matrix Recovery, p-Null Space Property, the Restricted Isometry Property
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.2,
February
29,
2024
ABSTRACT: A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.