A Deep Equilibrium Network for Hyperspectral Unmixing
This work addresses the high memory cost and limited spectral-spatial exploitation in unrolling-based deep learning methods for hyperspectral unmixing.
DEQ-Unmix reformulates hyperspectral unmixing as a deep equilibrium model, achieving superior unmixing performance on synthetic and real-world datasets while maintaining constant memory cost.
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.