· 2014
Weighted Nuclear Norm Minimization with Application to Image Denoising
- 2,271citations
- 2014year
Short summary
This paper introduces Weighted Nuclear Norm Minimization (WNNM), a novel approach that assigns different weights to singular values, enhancing flexibility over standard nuclear norm minimization. Applied to image denoising, WNNW significantly outperforms existing methods like BM3D.
AI-generated from the title and abstract; the full text is not read.
Key points
- Introduces Weighted Nuclear Norm Minimization (WNNM) for greater flexibility.
- Assigns different weights to singular values, unlike standard nuclear norm minimization.
- Applies WNNM to image denoising using nonlocal self-similarity.
- Outperforms BM3D and other state-of-the-art denoising algorithms.
AI-generated from the title and abstract; the full text is not read.
Abstract
As a convex relaxation of the low rank matrix factorization problem, the nuclear norm minimization has been attracting significant research interest in recent years. The standard nuclear norm minimization regularizes each singular value equally to pursue the convexity of the objective function. However, this greatly restricts its capability and flexibility in dealing with many practical problems (e.g., denoising), 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, where the singular values are assigned different weights. The solutions of the WNNM problem are analyzed under different weighting conditions. We then apply the proposed WNNM algorithm to image denoising by exploiting the image nonlocal self-similarity. Experimental results clearly show that the proposed WNNM algorithm outperforms many state-of-the-art denoising algorithms such as BM3D in terms of both quantitative measure and visual perception quality.
The authors' abstract, as published at the source., 2014 · DOI ↗
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Field: Computational Mechanics
Computational MechanicsEngineering