# Fast Noise Removal in Hyperspectral Images via Representative Coefficient Total Variation

arXiv: https://arxiv.org/abs/2211.01825 · HTML: https://mlsanity.com/paper/2211.01825/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 70 references that are in the map.
- First posted on arXiv 3 Nov 2022.

## Builds on (most cited first, 15 of 15)

- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition](https://mlsanity.com/paper/1707.02477/) (2017)
- [Hyperspectral Image Denoising Employing a Spatial-Spectral Deep Residual Convolutional Neural Network](https://mlsanity.com/paper/1806.00183/) (2018)
- [3D Quasi-Recurrent Neural Network for Hyperspectral Image Denoising](https://mlsanity.com/paper/2003.04547/) (2020)
- [Non-local Meets Global: An Iterative Paradigm for Hyperspectral Image Restoration](https://mlsanity.com/paper/2010.12921/) (2020)
- [Non-local Meets Global: An Integrated Paradigm for Hyperspectral Denoising](https://mlsanity.com/paper/1812.04243/) (2018)
- [Fast Hyperspectral Image Denoising and Inpainting Based on Low-Rank and Sparse Representations](https://mlsanity.com/paper/2103.06842/) (2021)
- [Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization](https://mlsanity.com/paper/1708.04181/) (2017)
- [A Trainable Spectral-Spatial Sparse Coding Model for Hyperspectral Image Restoration](https://mlsanity.com/paper/2111.09708/) (2021)
- [Denoising Hyperspectral Image with Non-i.i.d. Noise Structure](https://mlsanity.com/paper/1702.00098/) (2017)
- [Exact Decomposition of Joint Low Rankness and Local Smoothness Plus Sparse Matrices](https://mlsanity.com/paper/2201.12592/) (2022)
- [Total Variation Regularized Tensor RPCA for Background Subtraction from Compressive Measurements](https://mlsanity.com/paper/1503.01868/) (2015)
- [SMDS-Net: Model Guided Spectral-Spatial Network for Hyperspectral Image Denoising](https://mlsanity.com/paper/2012.01829/) (2020)
- [Low-rank Matrix Factorization under General Mixture Noise Distributions](https://mlsanity.com/paper/1601.01060/) (2016)

## Built on by (most cited first, 14 of 14)

- [Guaranteed Tensor Recovery Fused Low-rankness and Smoothness](https://mlsanity.com/paper/2302.02155/) (2023)
- [HIR-Diff: Unsupervised Hyperspectral Image Restoration Via Improved Diffusion Models](https://mlsanity.com/paper/2402.15865/) (2024)
- [HSIGene: A Foundation Model For Hyperspectral Image Generation](https://mlsanity.com/paper/2409.12470/) (2024)
- [Revisiting Nonlocal Self-Similarity from Continuous Representation](https://mlsanity.com/paper/2401.00708/) (2024)
- [PromptHSI: Universal Hyperspectral Image Restoration with Vision-Language Modulated Frequency Adaptation](https://mlsanity.com/paper/2411.15922/) (2024)
- [Pan-denoising: Guided Hyperspectral Image Denoising via Weighted Represent Coefficient Total Variation](https://mlsanity.com/paper/2407.06064/) (2024)
- [H2TF for Hyperspectral Image Denoising: Where Hierarchical Nonlinear Transform Meets Hierarchical Matrix Factorization](https://mlsanity.com/paper/2304.11141/) (2023)
- [Cross-Frequency Implicit Neural Representation with Self-Evolving Parameters](https://mlsanity.com/paper/2504.10929/) (2025)
- [Deep LoRA-Unfolding Networks for Image Restoration](https://mlsanity.com/paper/2602.18697/) (2026)
- [HIDFlowNet: A Flow-Based Deep Network for Hyperspectral Image Denoising](https://mlsanity.com/paper/2306.17797/) (2023)
- [Beyond Low-rankness: Guaranteed Matrix Recovery via Modified Nuclear Norm](https://mlsanity.com/paper/2507.18327/) (2025)
- [Spatial-Spectral Adaptive Fidelity and Noise Prior Reduction Guided Hyperspectral Image Denoising](https://mlsanity.com/paper/2604.12600/) (2026)
- [HIR-ALIGN: Enhancing Hyperspectral Image Restoration via Diffusion-Based Data Generation](https://mlsanity.com/paper/2605.13581/) (2026)
- [S3-PnP: Plug-and-Play Denoising for Scientific Imaging with Self-Supervised Score Priors](https://mlsanity.com/paper/2610.18458/) (2026)

## Abstract (arXiv)

Mining structural priors in data is a widely recognized technique for hyperspectral image (HSI) denoising tasks, whose typical ways include model-based methods and data-based methods. The model-based methods have good generalization ability, while the runtime cannot meet the fast processing requirements of the practical situations due to the large size of an HSI data  X ∈ ℝMN× B. For the data-based methods, they perform very fast on new test data once they have been trained. However, their generalization ability is always insufficient. In this paper, we propose a fast model-based HSI denoising approach. Specifically, we propose a novel regularizer named Representative Coefficient Total Variation (RCTV) to simultaneously characterize the low rank and local smooth properties. The RCTV regularizer is proposed based on the observation that the representative coefficient matrix U∈ℝMN× R (Rll B) obtained by orthogonally transforming the original HSI X can inherit the strong local-smooth prior of X. Since R/B is very small, the HSI denoising model based on the RCTV regularizer has lower time complexity. Additionally, we find that the representative coefficient matrix U is robust to noise, and thus the RCTV regularizer can somewhat promote the robustness of the HSI denoising model. Extensive experiments on mixed noise removal demonstrate the superiority of the proposed method both in denoising performance and denoising speed compared with other state-of-the-art methods. Remarkably, the denoising speed of our proposed method outperforms all the model-based techniques and is comparable with the deep learning-based approaches.