用深度平衡模型提升高光谱解混精度，同时保持内存恒定。
A Deep Equilibrium Network for Hyperspectral Unmixing
- 将解混问题建模为深度平衡点，用隐式微分实现恒定内存训练。
- 在合成与两个真实数据集上均达到更优解混性能。
- 适合需要高效训练且注重物理可解释性的遥感图像分析场景。
高光谱解混对分析高光谱图像至关重要，但准确解混仍具挑战性。传统方法难以有效建模复杂光谱-空间特征，深度学习方法常缺乏物理可解释性。基于展开的方法虽具网络可解释性，却未能充分挖掘光谱-空间信息，且反向传播中存在高内存消耗和数值精度问题。为此，我们提出DEQ-Unmix，将组分估计重新建模为深度平衡模型，通过隐式微分实现高效恒定内存训练。它用可训练的卷积网络替代数据重建项的梯度算子，以捕捉光谱-空间信息。借助隐式微分，DEQ-Unmix实现高效且恒定内存的反向传播。在合成数据及两个真实数据集上的实验表明，该方法在保持恒定内存开销的同时，实现了更优的解混性能。
原文摘要 · Abstract (English)
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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