Nonconvex Nonsmooth Low Rank Minimization via Iteratively Reweighted Nuclear Norm

By Canyi Lu, Jinhui Tang, Shuicheng Yan, Zhouchen Lin. IEEE Transactions on Image Processing, 2015

336 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Computational Mechanics, Media Technology

View Paper: https://www.semanticscholar.org/paper/9926961299b12741ce5eaa797e00032b5edf14b0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Shuicheng Yan
2. Jiashi Feng
3. Tao Mei
4. Yiquan Wu
5. Yimian Dai
6. Canyi Lu
7. Zhouchen Lin
8. Yi Yang

In Computational Mechanics

1. Zhouchen Lin
2. Canyi Lu
3. Jiashi Feng
4. Shuicheng Yan
5. Yimian Dai
6. Yiquan Wu
7. Tao Mei
8. René Vidal

In Media Technology

1. Yiquan Wu
2. Yimian Dai
3. Zhouchen Lin
4. Shuicheng Yan
5. Tao Mei
6. Jiashi Feng
7. Canyi Lu
8. Vishal M. Patel

Citations in the corpus

• Subspace Clustering by Block Diagonal Representation (2018, background): “semi-supervised learning and many other tasks [27], [41], [43].”
• Reweighted Infrared Patch-Tensor Model With Both Nonlocal and Local Priors for Single-Frame Small Target Detection (2017, methodology): “Inspired by it, many improved RPCA models have been proposed [39], [40], [41], [42].”