# Multi-channel Weighted Nuclear Norm Minimization for Real Color Image Denoising

arXiv: https://arxiv.org/abs/1705.09912 · HTML: https://mlsanity.com/paper/1705.09912/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2017.

## Built on by (most cited first, 30 of 41)

- [Physics-based Noise Modeling for Extreme Low-light Photography](https://mlsanity.com/paper/2108.02158/) (2021)
- [Efficient Diffusion Model for Image Restoration by Residual Shifting](https://mlsanity.com/paper/2403.07319/) (2024)
- [Adaptive Unfolding Total Variation Network for Low-Light Image Enhancement](https://mlsanity.com/paper/2110.00984/) (2021)
- [CVF-SID: Cyclic multi-Variate Function for Self-Supervised Image Denoising by Disentangling Noise from Image](https://mlsanity.com/paper/2203.13009/) (2022)
- [All-in-one Multi-degradation Image Restoration Network via Hierarchical Degradation Representation](https://mlsanity.com/paper/2308.03021/) (2023)
- [Exact Decomposition of Joint Low Rankness and Local Smoothness Plus Sparse Matrices](https://mlsanity.com/paper/2201.12592/) (2022)
- [Learn from Unpaired Data for Image Restoration: A Variational Bayes Approach](https://mlsanity.com/paper/2204.10090/) (2022)
- [Towards Adversarially Robust Deep Image Denoising](https://mlsanity.com/paper/2201.04397/) (2022)
- [DnLUT: Ultra-Efficient Color Image Denoising via Channel-Aware Lookup Tables](https://mlsanity.com/paper/2503.15931/) (2025)
- [Color Image Inpainting via Robust Pure Quaternion Matrix Completion: Error Bound and Weighted Loss](https://mlsanity.com/paper/2202.02063/) (2022)
- [Exploring and Evaluating Image Restoration Potential in Dynamic Scenes](https://mlsanity.com/paper/2203.11754/) (2022)
- [Joint Image Compression and Denoising via Latent-Space Scalability](https://mlsanity.com/paper/2205.01874/) (2022)
- [A Comparison of Image Denoising Methods](https://mlsanity.com/paper/2304.08990/) (2023)
- [Dual Residual Attention Network for Image Denoising](https://mlsanity.com/paper/2305.04269/) (2023)
- [Quaternion Nuclear Norm minus Frobenius Norm Minimization for color image reconstruction](https://mlsanity.com/paper/2409.07797/) (2024)
- [Multi-channel Nuclear Norm Minus Frobenius Norm Minimization for Color Image Denoising](https://mlsanity.com/paper/2209.08094/) (2022)
- [Unsupervised Image Denoising with Frequency Domain Knowledge](https://mlsanity.com/paper/2111.14362/) (2021)
- [Image Blind Denoising Using Dual Convolutional Neural Network with Skip Connection](https://mlsanity.com/paper/2304.01620/) (2023)
- [Image Denoising Using Green Channel Prior](https://mlsanity.com/paper/2408.05923/) (2024)
- [DCANet: Dual Convolutional Neural Network with Attention for Image Blind Denoising](https://mlsanity.com/paper/2304.01498/) (2023)
- [Self2Self+: Single-Image Denoising with Self-Supervised Learning and Image Quality Assessment Loss](https://mlsanity.com/paper/2307.10695/) (2023)
- [Feature-Align Network with Knowledge Distillation for Efficient Denoising](https://mlsanity.com/paper/2103.01524/) (2021)
- [Manifold Modeling in Quotient Space: Learning An Invariant Mapping with Decodability of Image Patches](https://mlsanity.com/paper/2203.05134/) (2022)
- [Generating Human Understandable Explanations for Node Embeddings](https://mlsanity.com/paper/2406.07642/) (2024)
- [FCNet: A Convolutional Neural Network for Arbitrary-Length Exposure Estimation](https://mlsanity.com/paper/2203.03624/) (2022)
- [Denoising single images by feature ensemble revisited](https://mlsanity.com/paper/2207.05176/) (2022)
- [Real Image Restoration via Structure-preserving Complementarity Attention](https://mlsanity.com/paper/2207.13879/) (2022)
- [Color Image Denoising Using The Green Channel Prior](https://mlsanity.com/paper/2402.08235/) (2024)
- [CAST-LUT: Tokenizer-Guided HSV Look-Up Tables for Purple Flare Removal](https://mlsanity.com/paper/2511.06764/) (2025)
- [Two-Stage Monte Carlo Denoising with Adaptive Sampling and Kernel Pool](https://mlsanity.com/paper/2103.16115/) (2021)

## Abstract (arXiv)

Most of the existing denoising algorithms are developed for grayscale images, while it is not a trivial work to extend them for color image denoising because the noise statistics in R, G, B channels can be very different for real noisy images. In this paper, we propose a multi-channel (MC) optimization model for real color image denoising under the weighted nuclear norm minimization (WNNM) framework. We concatenate the RGB patches to make use of the channel redundancy, and introduce a weight matrix to balance the data fidelity of the three channels in consideration of their different noise statistics. The proposed MC-WNNM model does not have an analytical solution. We reformulate it into a linear equality-constrained problem and solve it with the alternating direction method of multipliers. Each alternative updating step has closed-form solution and the convergence can be guaranteed. Extensive experiments on both synthetic and real noisy image datasets demonstrate the superiority of the proposed MC-WNNM over state-of-the-art denoising methods.