# Hyperspectral Image Denoising and Anomaly Detection Based on Low-rank and Sparse Representations

arXiv: https://arxiv.org/abs/2103.07437 · HTML: https://mlsanity.com/paper/2103.07437/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 54 references that are in the map.
- First posted on arXiv 12 Mar 2021.

## Builds on (most cited first, 3 of 3)

- [Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition](https://mlsanity.com/paper/1707.02477/) (2017)
- [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)

## Built on by (most cited first, 7 of 7)

- [FastHyMix: Fast and Parameter-free Hyperspectral Image Mixed Noise Removal](https://mlsanity.com/paper/2109.08879/) (2021)
- [Deep Learning Techniques for Hyperspectral Image Analysis in Agriculture: A Review](https://mlsanity.com/paper/2304.13880/) (2023)
- [Nonlocal Patch-Based Fully-Connected Tensor Network Decomposition for Remote Sensing Image Inpainting](https://mlsanity.com/paper/2109.05889/) (2021)
- [H2TF for Hyperspectral Image Denoising: Where Hierarchical Nonlinear Transform Meets Hierarchical Matrix Factorization](https://mlsanity.com/paper/2304.11141/) (2023)
- [Spectral-Spatial Extraction through Layered Tensor Decomposition for Hyperspectral Anomaly Detection](https://mlsanity.com/paper/2503.05183/) (2025)
- [Deep Equilibrium Convolutional Sparse Coding for Hyperspectral Image Denoising](https://mlsanity.com/paper/2508.15553/) (2025)
- [Multi-Modal Semantic Segmentation of Electrolyzer Components for Sustainable Hydrogen Technologies: A Dual-Branch Deep Learning Approach](https://mlsanity.com/paper/2607.16056/) (2026)

## Abstract (arXiv)

Hyperspectral imaging measures the amount of electromagnetic energy across the instantaneous field of view at a very high resolution in hundreds or thousands of spectral channels. This enables objects to be detected and the identification of materials that have subtle differences between them. However, the increase in spectral resolution often means that there is a decrease in the number of photons received in each channel, which means that the noise linked to the image formation process is greater. This degradation limits the quality of the extracted information and its potential applications. Thus, denoising is a fundamental problem in hyperspectral image (HSI) processing. As images of natural scenes with highly correlated spectral channels, HSIs are characterized by a high level of self-similarity and can be well approximated by low-rank representations. These characteristics underlie the state-of-the-art methods used in HSI denoising. However, where there are rarely occurring pixel types, the denoising performance of these methods is not optimal, and the subsequent detection of these pixels may be compromised. To address these hurdles, in this article, we introduce RhyDe (Robust hyperspectral Denoising), a powerful HSI denoiser, which implements explicit low-rank representation, promotes self-similarity, and, by using a form of collaborative sparsity, preserves rare pixels. The denoising and detection effectiveness of the proposed robust HSI denoiser is illustrated using semireal and real data.