Nonconvex Nonsmooth Low Rank Minimization via Iteratively Reweighted Nuclear Norm

—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 normbased 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 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 lim...

• Type: Journal
• Year: 2016
• Where: TIP
• Authors: Canyi Lu, Jinhui Tang, Shuicheng Yan, Zhouchen Lin
• Keywords: Education, TIP 2016