# A Deep Equilibrium Network for Hyperspectral Unmixing

arXiv: https://arxiv.org/abs/2604.11279 · HTML: https://mlsanity.com/paper/2604.11279/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 26 references that are in the map.
- First posted on arXiv 13 Apr 2026.

## Builds on (most cited first, 13 of 13)

- [CBAM: Convolutional Block Attention Module](https://mlsanity.com/paper/1807.06521/) (2018)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Understanding the Behaviour of Contrastive Loss](https://mlsanity.com/paper/2012.09740/) (2020)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [Spectral Variability in Hyperspectral Data Unmixing: A Comprehensive Review](https://mlsanity.com/paper/2001.07307/) (2020)
- [Nonlinear unmixing of hyperspectral images: models and algorithms](https://mlsanity.com/paper/1304.1875/) (2013)
- [Deep Hyperspectral Unmixing using Transformer Network](https://mlsanity.com/paper/2203.17076/) (2022)
- [A Plug-and-Play Priors Framework for Hyperspectral Unmixing](https://mlsanity.com/paper/2012.13074/) (2020)
- [Hyperspectral Unmixing Based on Nonnegative Matrix Factorization: A Comprehensive Review](https://mlsanity.com/paper/2205.09933/) (2022)
- [AE-RED: A Hyperspectral Unmixing Framework Powered by Deep Autoencoder and Regularization by Denoising](https://mlsanity.com/paper/2307.00269/) (2023)
- [Unrolling Plug-and-Play Network for Hyperspectral Unmixing](https://mlsanity.com/paper/2409.04719/) (2024)
- [DTU-Net: A Multi-Scale Dilated Transformer Network for Nonlinear Hyperspectral Unmixing](https://mlsanity.com/paper/2503.03465/) (2025)

## Abstract (arXiv)

Hyperspectral unmixing (HU) is crucial for analyzing hyperspectral imagery, yet achieving accurate unmixing remains challenging. While traditional methods struggle to effectively model complex spectral-spatial features, deep learning approaches often lack physical interpretability. Unrolling-based methods, despite offering network interpretability, inadequately exploit spectral-spatial information and incur high memory costs and numerical precision issues during backpropagation. To address these limitations, we propose DEQ-Unmix, which reformulates abundance estimation as a deep equilibrium model, enabling efficient constant-memory training via implicit differentiation. It replaces the gradient operator of the data reconstruction term with a trainable convolutional network to capture spectral-spatial information. By leveraging implicit differentiation, DEQ-Unmix enables efficient and constant-memory backpropagation. Experiments on synthetic and two real-world datasets demonstrate that DEQ-Unmix achieves superior unmixing performance while maintaining constant memory cost.