# Multi-channel Nuclear Norm Minus Frobenius Norm Minimization for Color Image Denoising

arXiv: https://arxiv.org/abs/2209.08094 · HTML: https://mlsanity.com/paper/2209.08094/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 55 references that are in the map.
- First posted on arXiv 16 Sep 2022.

## Builds on (most cited first, 12 of 12)

- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [Multi-channel Weighted Nuclear Norm Minimization for Real Color Image Denoising](https://mlsanity.com/paper/1705.09912/) (2017)
- [Weighted Schatten p-Norm Minimization for Image Denoising and Background Subtraction](https://mlsanity.com/paper/1512.01003/) (2015)
- [Fast L1-L2 minimization via a proximal operator](https://mlsanity.com/paper/1609.09530/) (2016)
- [External Prior Guided Internal Prior Learning for Real-World Noisy Image Denoising](https://mlsanity.com/paper/1705.04505/) (2017)
- [Large-Scale Low-Rank Matrix Learning with Nonconvex Regularizers](https://mlsanity.com/paper/1708.00146/) (2017)
- [Color Image and Multispectral Image Denoising Using Block Diagonal Representation](https://mlsanity.com/paper/1902.03954/) (2019)
- [Matrix Completion with Nonconvex Regularization: Spectral Operators and Scalable Algorithms](https://mlsanity.com/paper/1801.08227/) (2018)
- [Multiplicative Noise Removal: Nonlocal Low-Rank Model and Its Proximal Alternating Reweighted Minimization Algorithm](https://mlsanity.com/paper/2002.07633/) (2020)
- [Convergence rate analysis of primal-dual splitting schemes](https://mlsanity.com/paper/1408.4419/) (2014)

## Built on by (most cited first, 5 of 5)

- [Quaternion Nuclear Norm minus Frobenius Norm Minimization for color image reconstruction](https://mlsanity.com/paper/2409.07797/) (2024)
- [DCANet: Dual Convolutional Neural Network with Attention for Image Blind Denoising](https://mlsanity.com/paper/2304.01498/) (2023)
- [A Novel Truncated Norm Regularization Method for Multi-channel Color Image Denoising](https://mlsanity.com/paper/2307.07932/) (2023)
- [Matrix Completion Via Reweighted Logarithmic Norm Minimization](https://mlsanity.com/paper/2512.21050/) (2025)
- [Low-Rank Tensor Completion Based on Fractional Regularization with Ky Fan p-k Norm](https://mlsanity.com/paper/2606.19046/) (2026)

## Abstract (arXiv)

Color image denoising is frequently encountered in various image processing and computer vision tasks. One traditional strategy is to convert the RGB image to a less correlated color space and denoise each channel of the new space separately. However, such a strategy can not fully exploit the correlated information between channels and is inadequate to obtain satisfactory results. To address this issue, this paper proposes a new multi-channel optimization model for color image denoising under the nuclear norm minus Frobenius norm minimization framework. Specifically, based on the block-matching, the color image is decomposed into overlapping RGB patches. For each patch, we stack its similar neighbors to form the corresponding patch matrix. The proposed model is performed on the patch matrix to recover its noise-free version. During the recovery process, a) a weight matrix is introduced to fully utilize the noise difference between channels; b) the singular values are shrunk adaptively without additionally assigning weights. With them, the proposed model can achieve promising results while keeping simplicity. To solve the proposed model, an accurate and effective algorithm is built based on the alternating direction method of multipliers framework. The solution of each updating step can be analytically expressed in closed-from. Rigorous theoretical analysis proves the solution sequences generated by the proposed algorithm converge to their respective stationary points. Experimental results on both synthetic and real noise datasets demonstrate the proposed model outperforms state-of-the-art models.