# Fast Hyperspectral Image Denoising and Inpainting Based on Low-Rank and Sparse Representations

arXiv: https://arxiv.org/abs/2103.06842 · HTML: https://mlsanity.com/paper/2103.06842/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 54 references that are in the map.
- First posted on arXiv 11 Mar 2021.

## Builds on (most cited first, 1 of 1)

- [Blind image deblurring using class-adapted image priors](https://mlsanity.com/paper/1709.01710/) (2017)

## Built on by (most cited first, 30 of 39)

- [Spatial-Spectral Transformer for Hyperspectral Image Denoising](https://mlsanity.com/paper/2211.14090/) (2022)
- [Deep Plug-and-Play Prior for Hyperspectral Image Restoration](https://mlsanity.com/paper/2209.08240/) (2022)
- [Unsupervised Hyperspectral Pansharpening via Low-rank Diffusion Model](https://mlsanity.com/paper/2305.10925/) (2023)
- [SSUMamba: Spatial-Spectral Selective State Space Model for Hyperspectral Image Denoising](https://mlsanity.com/paper/2405.01726/) (2024)
- [FastHyMix: Fast and Parameter-free Hyperspectral Image Mixed Noise Removal](https://mlsanity.com/paper/2109.08879/) (2021)
- [Fast Noise Removal in Hyperspectral Images via Representative Coefficient Total Variation](https://mlsanity.com/paper/2211.01825/) (2022)
- [Hyperspectral and multispectral image fusion with arbitrary resolution through self-supervised representations](https://mlsanity.com/paper/2405.17818/) (2024)
- [Hyperspectral Image Denoising and Anomaly Detection Based on Low-rank and Sparse Representations](https://mlsanity.com/paper/2103.07437/) (2021)
- [A Comparison of Image Denoising Methods](https://mlsanity.com/paper/2304.08990/) (2023)
- [PromptHSI: Universal Hyperspectral Image Restoration with Vision-Language Modulated Frequency Adaptation](https://mlsanity.com/paper/2411.15922/) (2024)
- [Hyperspectral Image Denoising via Spatial-Spectral Recurrent Transformer](https://mlsanity.com/paper/2401.03885/) (2023)
- [Hyperspectral Image Denoising Using Non-convex Local Low-rank and Sparse Separation with Spatial-Spectral Total Variation Regularization](https://mlsanity.com/paper/2201.02812/) (2022)
- [Degradation-Noise-Aware Deep Unfolding Transformer for Hyperspectral Image Denoising](https://mlsanity.com/paper/2305.04047/) (2023)
- [Connections between Deep Equilibrium and Sparse Representation Models with Application to Hyperspectral Image Denoising](https://mlsanity.com/paper/2203.15901/) (2022)
- [Multi-scale Adaptive Fusion Network for Hyperspectral Image Denoising](https://mlsanity.com/paper/2304.09373/) (2023)
- [HADAR-Based Thermal Infrared Hyperspectral Image Restoration](https://mlsanity.com/paper/2605.13664/) (2026)
- [HyDe: The First Open-Source, Python-Based, GPU-Accelerated Hyperspectral Denoising Package](https://mlsanity.com/paper/2204.06979/) (2022)
- [Real-Time Compressed Sensing for Joint Hyperspectral Image Transmission and Restoration for CubeSat](https://mlsanity.com/paper/2404.15781/) (2024)
- [Bayesian Robust Tensor Ring Model for Incomplete Multiway Data](https://mlsanity.com/paper/2202.13321/) (2022)
- [Beam-Shape Effects and Noise Removal from THz Time-Domain Images in Reflection Geometry in the 0.25-6 THz Range](https://mlsanity.com/paper/2203.00417/) (2022)
- [EigenSR: Eigenimage-Bridged Pre-Trained RGB Learners for Single Hyperspectral Image Super-Resolution](https://mlsanity.com/paper/2409.04050/) (2024)
- [Mixture-Net: Low-Rank Deep Image Prior Inspired by Mixture Models for Spectral Image Recovery](https://mlsanity.com/paper/2211.02973/) (2022)
- [Self-Supervised Hyperspectral Inpainting with the Optimisation inspired Deep Neural Network Prior](https://mlsanity.com/paper/2306.07308/) (2023)
- [Self-supervised Deep Hyperspectral Inpainting with the Sparsity and Low-Rank Considerations](https://mlsanity.com/paper/2306.08128/) (2023)
- [Self-supervised Deep Hyperspectral Inpainting with the Plug and Play and Deep Image Prior Models](https://mlsanity.com/paper/2501.08195/) (2025)
- [LRDUN: A Low-Rank Deep Unfolding Network for Efficient Spectral Compressive Imaging](https://mlsanity.com/paper/2511.18513/) (2025)
- [Scalable neural pushbroom architectures for real-time denoising of hyperspectral images onboard satellites](https://mlsanity.com/paper/2601.05020/) (2026)
- [SHARE: A Fully Unsupervised Framework for Single Hyperspectral Image Restoration](https://mlsanity.com/paper/2601.13987/) (2026)
- [TeX-1500: A Paired Real-World LWIR Hyperspectral Dataset and Benchmark for Temperature-Emissivity-Texture Decomposition](https://mlsanity.com/paper/2606.03806/) (2026)
- [Multi-modal and frequency-weighted tensor nuclear norm for hyperspectral image denoising](https://mlsanity.com/paper/2106.12489/) (2021)

## Abstract (arXiv)

This paper introduces two very fast and competitive hyperspectral image (HSI) restoration algorithms: fast hyperspectral denoising (FastHyDe), a denoising algorithm able to cope with Gaussian and Poissonian noise, and fast hyperspectral inpainting (FastHyIn), an inpainting algorithm to restore HSIs where some observations from known pixels in some known bands are missing. FastHyDe and FastHyIn fully exploit extremely compact and sparse HSI representations linked with their low-rank and self-similarity characteristics. In a series of experiments with simulated and real data, the newly introduced FastHyDe and FastHyIn compete with the state-of-the-art methods, with much lower computational complexity.