Title: An optimal condition of robust low-rank matrices recovery

Authors: Jianwen Huang; Sanfu Wang; Jianjun Wang; Feng Zhang; Hailin Wang; Jinping Jia

Addresses: School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, China ' School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, China ' School of Mathematics and Statistics, Southwest University, Beibei District, Chongqing 400715, China; School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China ' School of Mathematics and Statistics, Southwest University, Beibei District, Chongqing 400715, China ' School of Mathematics and Statistics, Southwest University, Beibei District, Chongqing 400715, China ' School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, China

Abstract: In this paper we investigate the reconstruction conditions of nuclear norm minimisation for low-rank matrix recovery. We obtain a sufficient condition to guarantee the robust reconstruction and exact reconstruction of all r-rank matrices from linear measurements via nuclear norm minimisation. Furthermore, we not only show that our result could return to previous result, but also demonstrate that the gained upper bounds concerning the recovery error are better. Moreover, we prove that the restricted isometry property condition is sharp. Besides, the numerical experiments are conducted to reveal the nuclear norm minimisation method is stable and robust for the recovery of low-rank matrix.

Keywords: low-rank matrix recovery; nuclear norm minimisation; restricted isometry property condition; compressed sensing; convex optimisation.

DOI: 10.1504/IJWMC.2021.119055

International Journal of Wireless and Mobile Computing, 2021 Vol.21 No.1, pp.11 - 25

Received: 20 Aug 2020
Accepted: 14 Sep 2020

Published online: 13 Nov 2021 *

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