A Deep Equilibrium Network for Hyperspectral Unmixing

TL;DR

DEQ-Unmix introduces a deep equilibrium model for hyperspectral unmixing, improving spectral-spatial feature modeling with efficient constant-memory training and superior performance on real datasets.

Contribution

It reformulates abundance estimation as a deep equilibrium model, replacing gradient operators with trainable networks and enabling efficient implicit differentiation-based training.

Findings

Achieves superior unmixing performance on synthetic and real datasets.

Maintains constant memory cost during training.

Effectively models spectral-spatial features with a trainable convolutional network.

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.