Year: 2015
Type: article
Abstract: 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 L0-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 re-weighted 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.
Authors: Canyi Lu, Jinhui Tang, Shuicheng Yan, Zhouchen Lin
Language: English
Subfield: Signal Processing
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funders: Microsoft Research, Northeast Normal University, National Research Foundation, National University of Singapore, National Research Foundation Singapore, National Natural Science Foundation of China, Chinese Academy of Sciences, Ministry of Education, India, Beijing Jiaotong University, Nanjing University of Science and Technology, Peking University, Nanjing University, Southeast University, Fuzhou University, University of Science and Technology of China, University of California, Irvine, Microsoft Research Asia, Institute of Computing Technology, Chinese Academy of Sciences, National Key Research and Development Program of China
OpenAlex ID: W1860736741