A Deep Equilibrium Network for Hyperspectral Unmixing

2026-04-13

AI Summary

This work addresses key challenges in hyperspectral unmixing, including the difficulty of modeling spectral-spatial features, the lack of physical interpretability in existing deep learning methods, and the high memory cost and inaccurate backpropagation associated with unfolded models. To overcome these limitations, the study introduces deep equilibrium models to hyperspectral unmixing for the first time. By leveraging implicit differentiation, the proposed approach enables constant-memory training and replaces conventional gradient terms with trainable convolutional operators, effectively integrating spectral and spatial information. The method achieves a favorable balance between physical interpretability and computational efficiency, delivering state-of-the-art unmixing accuracy on both synthetic and two real-world hyperspectral datasets while significantly reducing memory consumption.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Search and Optimization: Mixed Discrete/Continuous Search
• Computer Vision: Diffusion Models for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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.

Problem

• Hyperspectral unmixing
• spectral-spatial features
• physical interpretability
• memory cost
• numerical precision

Innovation

• Deep Equilibrium Model
• Hyperspectral Unmixing
• Implicit Differentiation
• Spectral-Spatial Feature Learning
• Constant-Memory Training