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 | |
【 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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