用对称性训练无真值图像重建模型，提升效果且简化反向传播。
Equivariant Deep Equilibrium Models for Imaging Inverse Problems
- 利用信号对称性设计损失函数，无需真实图像数据
- 通过隐式微分训练深度均衡模型，性能优于基线方法
- 模型近似不变先验的邻近算子，适合无监督图像重建
等变成像（EI）可通过利用信号对称性，在无需真实数据的情况下训练信号重建模型。深度均衡模型（DEQs）是一类神经网络，其输出为学习算子的不动点。然而，使用复杂EI损失训练DEQs需要对不动点计算进行隐式微分，实现较为困难。本文表明反向传播可模块化实现，简化了训练过程。实验显示，采用隐式微分训练的DEQs优于基于雅可比自由反向传播及其他基线方法。此外，我们发现经EI训练的DEQs近似于不变先验的邻近映射。
原文摘要 · Abstract (English)
Equivariant imaging (EI) enables training signal reconstruction models without requiring ground truth data by leveraging signal symmetries. Deep equilibrium models (DEQs) are a powerful class of neural networks where the output is a fixed point of a learned operator. However, training DEQs with complex EI losses requires implicit differentiation through fixed-point computations, whose implementation can be challenging. We show that backpropagation can be implemented modularly, simplifying training. Experiments demonstrate that DEQs trained with implicit differentiation outperform those trained with Jacobian-free backpropagation and other baseline methods. Additionally, we find evidence that EI-trained DEQs approximate the proximal map of an invariant prior.
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