Exact recovery low-rank matrix via transformed affine matrix rank minimization

NEUROCOMPUTING

卷:319

Article

Cui, Angang¹  Peng, Jigen²  Li, Haiyang³ 

[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China

[2] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China

[3] Xian Polytech Univ, Sch Sci, Xian 710048, Shaanxi, Peoples R China

关键词: Affine matrix rank minimization;    Transformed affine matrix rank minimization;    Non-convex fraction function;    Equivalence;    DC algorithm;   

DOI  :  10.1016/j.neucom.2018.05.092

来源: Elsevier

【 摘 要 】

The goal of affine matrix rank minimization problem is to reconstruct a low-rank or approximately low-rank matrix under linear constraints. In general, this problem is combinatorial and NP-hard. In this paper, a nonconvex fraction function is studied to approximate the rank of a matrix and translate this NP-hard problem into a transformed affine matrix rank minimization problem. The equivalence between these two problems is established, and we proved that the uniqueness of the global minimizer of transformed affine matrix rank minimization problem also solves affine matrix rank minimization problem if some conditions are satisfied. Moreover, we also proved that the optimal solution to the transformed affine matrix rank minimization problem can be approximately obtained by solving its regularization problem for some proper smaller lambda > 0. Lastly, the DC algorithm is utilized to solve the regularization transformed affine matrix rank minimization problem and the numerical experiments on image inpainting problems show that our method performs effectively in recovering low-rank images compared with some state-of-art algorithms. (c) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free