A Deep Equilibrium Network for Hyperspectral Unmixing

• URL: http://arxiv.org/abs/2604.11279v1
• Date: Mon, 13 Apr 2026 10:38:28 GMT
• Title: A Deep Equilibrium Network for Hyperspectral Unmixing
• Abstract summary: We propose DEQ-Unmix, which reformulates abundance estimation as a deep equilibrium model.<n>It replaces the operator of the data reconstruction term with a trainable convolutional network to capture spectral-spatial information.<n>Experiments on synthetic and two real-world datasets demonstrate that DEQ-Unmix achieves superior unmixing performance while maintaining constant memory cost.
• Score: 15.1730669896454
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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