Nonconvex Nonsmooth Low Rank Minimization via Iteratively Reweighted   Nuclear Norm

doi:10.1109/TIP.2015.2511584

CORC > 北京大学 > 信息科学技术学院

	Nonconvex Nonsmooth Low Rank Minimization via Iteratively Reweighted Nuclear Norm
	Lu, Canyi ; Tang, Jinhui ; Yan, Shuicheng ; Lin, Zhouchen
刊名	IEEE TRANSACTIONS ON IMAGE PROCESSING
	2016
关键词	Nonconvex low rank minimization iteratively reweighted nuclear norm algorithm LEAST-SQUARES MINIMIZATION MATRIX COMPLETION THRESHOLDING ALGORITHM SPARSE REPRESENTATION VARIABLE SELECTION FACE RECOGNITION REGULARIZATION RECOVERY SEGMENTATION SYSTEMS
DOI	10.1109/TIP.2015.2511584
英文摘要	The nuclear norm is widely used as a convex surrogate of the rank function in compressive sensing for low rank matrix recovery with its applications in image recovery and signal processing. However, solving the nuclear norm-based relaxed convex problem usually leads to a suboptimal solution of the original rank minimization problem. In this paper, we propose to use a family of nonconvex surrogates of L-0-norm on the singular values of a matrix to approximate the rank function. This leads to a nonconvex nonsmooth minimization problem. Then, we propose to solve the problem by an iteratively reweighted nuclear norm (IRNN) algorithm. IRNN iteratively solves a weighted singular value thresholding problem, which has a closed form solution due to the special properties of the nonconvex surrogate functions. We also extend IRNN to solve the nonconvex problem with two or more blocks of variables. In theory, we prove that the IRNN decreases the objective function value monotonically, and any limit point is a stationary point. Extensive experiments on both synthesized data and real images demonstrate that IRNN enhances the low rank matrix recovery compared with the state-of-the-art convex algorithms.; Singapore National Research Foundation under its International Research Centre, Singapore Funding Initiative; National Basic Research Program of China (973 Program) [2015CB352502]; National Natural Science Foundation (NSF) of China [61272341, 61231002]; Microsoft Research Asia Collaborative Research Program; SCI(E); ARTICLE; canyilu@gmail.com; jinhuitang@mail.njust.edu.cn; eleyans@nus.edu.sg; zlin@pku.edu.cn; 2; 829-839; 25
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/457005]
专题	信息科学技术学院
推荐引用方式 GB/T 7714	Lu, Canyi,Tang, Jinhui,Yan, Shuicheng,et al. Nonconvex Nonsmooth Low Rank Minimization via Iteratively Reweighted Nuclear Norm[J]. IEEE TRANSACTIONS ON IMAGE PROCESSING,2016.
APA	Lu, Canyi,Tang, Jinhui,Yan, Shuicheng,&Lin, Zhouchen.(2016).Nonconvex Nonsmooth Low Rank Minimization via Iteratively Reweighted Nuclear Norm.IEEE TRANSACTIONS ON IMAGE PROCESSING.
MLA	Lu, Canyi,et al."Nonconvex Nonsmooth Low Rank Minimization via Iteratively Reweighted Nuclear Norm".IEEE TRANSACTIONS ON IMAGE PROCESSING (2016).