# Hyperspectral Denoising Using Unsupervised Disentangled Spatio-Spectral Deep Priors

arXiv: https://arxiv.org/abs/2102.12310 · HTML: https://mlsanity.com/paper/2102.12310/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 61 references that are in the map.
- First posted on arXiv 24 Feb 2021.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Image Restoration using Total Variation Regularized Deep Image Prior](https://mlsanity.com/paper/1810.12864/) (2018)
- [Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition](https://mlsanity.com/paper/1707.02477/) (2017)
- [A Multi-Scale and Multi-Depth Convolutional Neural Network for Remote Sensing Imagery Pan-Sharpening](https://mlsanity.com/paper/1712.09809/) (2017)
- [Hyperspectral Image Denoising Employing a Spatial-Spectral Deep Residual Convolutional Neural Network](https://mlsanity.com/paper/1806.00183/) (2018)
- [Deep Hyperspectral Prior: Denoising, Inpainting, Super-Resolution](https://mlsanity.com/paper/1902.00301/) (2019)
- [Weighted Low-rank Tensor Recovery for Hyperspectral Image Restoration](https://mlsanity.com/paper/1709.00192/) (2017)
- [Hyperspectral Super-Resolution: A Coupled Tensor Factorization Approach](https://mlsanity.com/paper/1804.05307/) (2018)
- [Denoising Hyperspectral Image with Non-i.i.d. Noise Structure](https://mlsanity.com/paper/1702.00098/) (2017)
- [Hybrid Noise Removal in Hyperspectral Imagery With a Spatial-Spectral Gradient Network](https://mlsanity.com/paper/1810.00495/) (2018)
- [Semiblind Hyperspectral Unmixing in the Presence of Spectral Library Mismatches](https://mlsanity.com/paper/1507.01661/) (2015)
- [Self-Dictionary Sparse Regression for Hyperspectral Unmixing: Greedy Pursuit and Pure Pixel Search are Related](https://mlsanity.com/paper/1409.4320/) (2014)
- [Inexact Block Coordinate Descent Methods For Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/1607.03092/) (2016)

## Built on by (most cited first, 12 of 12)

- [HyperSIGMA: Hyperspectral Intelligence Comprehension Foundation Model](https://mlsanity.com/paper/2406.11519/) (2024)
- [EDiffSR: An Efficient Diffusion Probabilistic Model for Remote Sensing Image Super-Resolution](https://mlsanity.com/paper/2310.19288/) (2023)
- [DDS2M: Self-Supervised Denoising Diffusion Spatio-Spectral Model for Hyperspectral Image Restoration](https://mlsanity.com/paper/2303.06682/) (2023)
- [FastHyMix: Fast and Parameter-free Hyperspectral Image Mixed Noise Removal](https://mlsanity.com/paper/2109.08879/) (2021)
- [HyperFree: A Channel-adaptive and Tuning-free Foundation Model for Hyperspectral Remote Sensing Imagery](https://mlsanity.com/paper/2503.21841/) (2025)
- [Nonlinear Transform Induced Tensor Nuclear Norm for Tensor Completion](https://mlsanity.com/paper/2110.08774/) (2021)
- [Variational Zero-shot Multispectral Pansharpening](https://mlsanity.com/paper/2407.06633/) (2024)
- [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)
- [HSI-VAR: Rethinking Hyperspectral Restoration through Spatial-Spectral Visual Autoregression](https://mlsanity.com/paper/2602.00749/) (2026)
- [Multi-modal and frequency-weighted tensor nuclear norm for hyperspectral image denoising](https://mlsanity.com/paper/2106.12489/) (2021)
- [Compressive Imaging Reconstruction via Tensor Decomposed Multi-Resolution Grid Encoding](https://mlsanity.com/paper/2507.07707/) (2025)

## Abstract (arXiv)

Image denoising is often empowered by accurate prior information. In recent years, data-driven neural network priors have shown promising performance for RGB natural image denoising. Compared to classic handcrafted priors (e.g., sparsity and total variation), the "deep priors" are learned using a large number of training samples -- which can accurately model the complex image generating process. However, data-driven priors are hard to acquire for hyperspectral images (HSIs) due to the lack of training data. A remedy is to use the so-called unsupervised deep image prior (DIP). Under the unsupervised DIP framework, it is hypothesized and empirically demonstrated that proper neural network structures are reasonable priors of certain types of images, and the network weights can be learned without training data. Nonetheless, the most effective unsupervised DIP structures were proposed for natural images instead of HSIs. The performance of unsupervised DIP-based HSI denoising is limited by a couple of serious challenges, namely, network structure design and network complexity. This work puts forth an unsupervised DIP framework that is based on the classic spatio-spectral decomposition of HSIs. Utilizing the so-called linear mixture model of HSIs, two types of unsupervised DIPs, i.e., U-Net-like network and fully-connected networks, are employed to model the abundance maps and endmembers contained in the HSIs, respectively. This way, empirically validated unsupervised DIP structures for natural images can be easily incorporated for HSI denoising. Besides, the decomposition also substantially reduces network complexity. An efficient alternating optimization algorithm is proposed to handle the formulated denoising problem. Semi-real and real data experiments are employed to showcase the effectiveness of the proposed approach.