# Color Image and Multispectral Image Denoising Using Block Diagonal Representation

arXiv: https://arxiv.org/abs/1902.03954 · HTML: https://mlsanity.com/paper/1902.03954/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2019.

## Built on by (most cited first, 10 of 10)

- [Unidirectional Video Denoising by Mimicking Backward Recurrent Modules with Look-ahead Forward Ones](https://mlsanity.com/paper/2204.05532/) (2022)
- [A Comparison of Image Denoising Methods](https://mlsanity.com/paper/2304.08990/) (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)
- [Image Denoising Using Green Channel Prior](https://mlsanity.com/paper/2408.05923/) (2024)
- [Fast and Robust Sparsity-Aware Block Diagonal Representation](https://mlsanity.com/paper/2312.01137/) (2023)
- [Color Image Denoising Using The Green Channel Prior](https://mlsanity.com/paper/2402.08235/) (2024)
- [A Novel Truncated Norm Regularization Method for Multi-channel Color Image Denoising](https://mlsanity.com/paper/2307.07932/) (2023)
- [Efficient Image Denoising Using Global and Local Circulant Representation](https://mlsanity.com/paper/2508.10307/) (2025)
- [Image Denoising Using Global and Local Circulant Representation](https://mlsanity.com/paper/2512.23569/) (2025)

## Abstract (arXiv)

Filtering images of more than one channel is challenging in terms of both efficiency and effectiveness. By grouping similar patches to utilize the self-similarity and sparse linear approximation of natural images, recent nonlocal and transform-domain methods have been widely used in color and multispectral image (MSI) denoising. Many related methods focus on the modeling of group level correlation to enhance sparsity, which often resorts to a recursive strategy with a large number of similar patches. The importance of the patch level representation is understated. In this paper, we mainly investigate the influence and potential of representation at patch level by considering a general formulation with block diagonal matrix. We further show that by training a proper global patch basis, along with a local principal component analysis transform in the grouping dimension, a simple transform-threshold-inverse method could produce very competitive results. Fast implementation is also developed to reduce computational complexity. Extensive experiments on both simulated and real datasets demonstrate its robustness, effectiveness and efficiency.