Guarantees of Fast Band Restricted Thresholding Algorithm for Low-Rank Matrix Recovery Problem. (30th April 2020)

• Record Type: Journal Article
• Authors: Zhao, Fujun; Peng, Jigen; Sun, Kai; Cui, Angang
• Other Names: Shi Junpeng Guest Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2020(2020)
• Publication Date: 2020-04-30
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2020/9578168
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : Affine matrix rank minimization problem is a famous problem with a wide range of application backgrounds. This problem is a combinatorial problem and deemed to be NP-hard. In this paper, we propose a family of fast band restricted thresholding (FBRT) algorithms for low rank matrix recovery from a small number of linear measurements. Characterized via restricted isometry constant, we elaborate the theoretical guarantees in both noise-free and noisy cases. Two thresholding operators are discussed and numerical demonstrations show that FBRT algorithms have better performances than some state-of-the-art methods. Particularly, the running time of FBRT algorithms is much faster than the commonly singular value thresholding algorithms.