A non-convex approach to low-rank and sparse matrix decomposition
Optimization and Control
2019-05-14 v2 Computer Vision and Pattern Recognition
Image and Video Processing
Abstract
In this paper, we develop a nonconvex approach to the problem of low-rank and sparse matrix decomposition. In our nonconvex method, we replace the rank function and the -norm of a given matrix with a non-convex fraction function on the singular values and the elements of the matrix respectively. An alternative direction method of multipliers algorithm is utilized to solve our proposed nonconvex problem with the nonconvex fraction function penalty. Numerical experiments on some low-rank and sparse matrix decomposition problems show that our method performs very well in recovering low-rank matrices which are heavily corrupted by large sparse errors.
Cite
@article{arxiv.1807.01276,
title = {A non-convex approach to low-rank and sparse matrix decomposition},
author = {Angang Cui and Meng Wen and Haiyang Li and Jigen Peng},
journal= {arXiv preprint arXiv:1807.01276},
year = {2019}
}