Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision

View Researcher's Other Codes

MATLAB code for the paper: “Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision”.

Disclaimer: The provided code links for this paper are external links. Science Nest has no responsibility for the accuracy, legality or content of these links. Also, by downloading this code(s), you agree to comply with the terms of use as set out by the author(s) of the code(s).

Please contact us in case of a broken link from here

This paper has multiple code variations. You can add them one by one to the cart. After adding the first one to the cart, use the “back” button in your browser and add the next one, and so on.

Download
Authors Shuhang Gu, Qi Xie, Deyu Meng, Wangmeng Zuo, Xiangchu Feng, and ´╗┐Lei Zhang
Journal/Conference Name International Journal of Computer Vision
Paper Category
Paper Abstract As a convex relaxation of the rank minimization model, the nuclear norm minimization (NNM) problem has been attracting significant research interest in recent years. The standard NNM regularizes each singular value equally, composing an easily calculated convex norm. However, this restricts its capability and flexibility in dealing with many practical problems, where the singular values have clear physical meanings and should be treated differently. In this paper we study the weighted nuclear norm minimization (WNNM) problem, which adaptively assigns weights on different singular values. As the key step of solving general WNNM models, the theoretical properties of the weighted nuclear norm proximal (WNNP) operator are investigated. Albeit nonconvex, we prove that WNNP is equivalent to a standard quadratic programming problem with linear con-strains, which facilitates solving the original problem with off-the-shelf convex optimization solvers. In particular, when the weights are sorted in a non-descending order, its optimal solution can be easily obtained in closed-form. With WNNP, the solving strategies for multiple extensions of WNNM, including robust PCA and matrix completion, can be readily constructed under the alternating direction method of multipliers paradigm. Furthermore, inspired by the reweighted sparse coding scheme, we present an automatic weight setting method, which greatly facilitates the practical implementation of WNNM. The proposed WNNM methods achieve state-of-the-art performance in typical low level vision tasks, including image denoising, background subtraction and image inpainting.
Date of publication 2017
Code Programming Language MATLAB
Comment

Copyright Researcher 2021