期刊论文详细信息
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 卷:336
Affine matrix rank minimization problem via non-convex fraction function penalty
Article
Cui, Angang1  Peng, Jigen2  Li, Haiyang3  Zhang, Chengyi3  Yu, Yongchao1 
[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;    Low-rank;    Matrix completion;    Fraction function;    Iterative singular value thresholding algorithm;    Image inpainting;   
DOI  :  10.1016/j.cam.2017.12.048
来源: Elsevier
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【 摘 要 】

Affine matrix rank minimization problem is a fundamental problem in many important applications. It is well known that this problem is combinatorial and NP-hard in general. In this paper, a continuous promoting low rank non-convex fraction function is studied to replace the rank function in this NP-hard problem. An iterative singular value thresholding algorithm is proposed to solve the regularization transformed affine matrix rank minimization problem. With the change of the parameter in non-convex fraction function, we could get some much better results, which is one of the advantages for the iterative singular value thresholding algorithm compared with some state-of-art methods. Some convergence results are established. Moreover, we proved that the value of the regularization parameter lambda > 0 cannot be chosen too large. Indeed, there exists (lambda) over bar > 0 such that the optimal solution of the regularization transformed affine matrix rank minimization problem is equal to zero for any lambda > (lambda) over bar. Numerical experiments on matrix completion problems and image inpainting problems show that our method performs effective in finding a low-rank matrix compared with some state-of-art methods. (C) 2018 Elsevier B.V. All rights reserved.

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