# Non-local Meets Global: An Integrated Paradigm for Hyperspectral Denoising

arXiv: https://arxiv.org/abs/1812.04243 · HTML: https://mlsanity.com/paper/1812.04243/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Dec 2018.

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

- [HyperSIGMA: Hyperspectral Intelligence Comprehension Foundation Model](https://mlsanity.com/paper/2406.11519/) (2024)
- [HIR-Diff: Unsupervised Hyperspectral Image Restoration Via Improved Diffusion Models](https://mlsanity.com/paper/2402.15865/) (2024)
- [Spectral Enhanced Rectangle Transformer for Hyperspectral Image Denoising](https://mlsanity.com/paper/2304.00844/) (2023)
- [A Trainable Spectral-Spatial Sparse Coding Model for Hyperspectral Image Restoration](https://mlsanity.com/paper/2111.09708/) (2021)
- [Spatial-Spectral Transformer for Hyperspectral Image Denoising](https://mlsanity.com/paper/2211.14090/) (2022)
- [DDS2M: Self-Supervised Denoising Diffusion Spatio-Spectral Model for Hyperspectral Image Restoration](https://mlsanity.com/paper/2303.06682/) (2023)
- [Deep Plug-and-Play Prior for Hyperspectral Image Restoration](https://mlsanity.com/paper/2209.08240/) (2022)
- [HyperFree: A Channel-adaptive and Tuning-free Foundation Model for Hyperspectral Remote Sensing Imagery](https://mlsanity.com/paper/2503.21841/) (2025)
- [Hybrid Spectral Denoising Transformer with Guided Attention](https://mlsanity.com/paper/2303.09040/) (2023)
- [Fast Noise Removal in Hyperspectral Images via Representative Coefficient Total Variation](https://mlsanity.com/paper/2211.01825/) (2022)
- [Tensor Decompositions for Hyperspectral Data Processing in Remote Sensing: A Comprehensive Review](https://mlsanity.com/paper/2205.06407/) (2022)
- [Hybrid Convolutional and Attention Network for Hyperspectral Image Denoising](https://mlsanity.com/paper/2403.10067/) (2024)
- [Mixed Attention Network for Hyperspectral Image Denoising](https://mlsanity.com/paper/2301.11525/) (2023)
- [In2SET: Intra-Inter Similarity Exploiting Transformer for Dual-Camera Compressive Hyperspectral Imaging](https://mlsanity.com/paper/2312.13319/) (2023)
- [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)
- [Real Noise Decoupling for Hyperspectral Image Denoising](https://mlsanity.com/paper/2511.17196/) (2025)
- [Nonlocal Patch-Based Fully-Connected Tensor Network Decomposition for Remote Sensing Image Inpainting](https://mlsanity.com/paper/2109.05889/) (2021)
- [MP-HSIR: A Multi-Prompt Framework for Universal Hyperspectral Image Restoration](https://mlsanity.com/paper/2503.09131/) (2025)
- [Degradation-Noise-Aware Deep Unfolding Transformer for Hyperspectral Image Denoising](https://mlsanity.com/paper/2305.04047/) (2023)
- [Enhancing Unregistered Hyperspectral Image Super-Resolution via Unmixing-based Abundance Fusion Learning](https://mlsanity.com/paper/2603.07918/) (2026)
- [STAR-Net: An Interpretable Model-Aided Network for Remote Sensing Image Denoising](https://mlsanity.com/paper/2505.24327/) (2025)
- [Low-Light Hyperspectral Image Enhancement](https://mlsanity.com/paper/2208.03042/) (2022)
- [Hybrid Spatial-spectral Neural Network for Hyperspectral Image Denoising](https://mlsanity.com/paper/2406.08782/) (2024)
- [SSCAN: A Spatial-spectral Cross Attention Network for Hyperspectral Image Denoising](https://mlsanity.com/paper/2105.10949/) (2021)
- [Low-rank Tensor Learning with Nonconvex Overlapped Nuclear Norm Regularization](https://mlsanity.com/paper/2205.03059/) (2022)
- [Color Image Denoising Using The Green Channel Prior](https://mlsanity.com/paper/2402.08235/) (2024)
- [Hyperspectral Mixed Noise Removal via Subspace Representation and Weighted Low-rank Tensor Regularization](https://mlsanity.com/paper/2111.07044/) (2021)
- [Latent Matrices for Tensor Network Decomposition and to Tensor Completion](https://mlsanity.com/paper/2210.03392/) (2022)

## Abstract (arXiv)

Non-local low-rank tensor approximation has been developed as a state-of-the-art method for hyperspectral image (HSI) denoising. Unfortunately, with more spectral bands for HSI, while the running time of these methods significantly increases, their denoising performance benefits little. In this paper, we claim that the HSI underlines a global spectral low-rank subspace, and the spectral subspaces of each full band patch groups should underlie this global low-rank subspace. This motivates us to propose a unified spatial-spectral paradigm for HSI denoising. As the new model is hard to optimize, we further propose an efficient algorithm for optimization, which is motivated by alternating minimization. This is done by first learning a low-dimensional projection and the related reduced image from the noisy HSI. Then, the non-local low-rank denoising and iterative regularization are developed to refine the reduced image and projection, respectively. Finally, experiments on synthetic and both real datasets demonstrate the superiority against the other state-of-the-arts HSI denoising methods.