通过图像网格的置换机制，实现可训练的稳定去噪器，保障图像重建全局收敛。
Trainable Nonexpansive Denoisers for Contractive Image Reconstruction
- 利用图像网格的置换对称性设计非扩张神经架构
- 在超分辨率与去模糊任务中达到与基线相当的性能
- 首次实现可训练去噪器的全局利普希茨约束保障
具有利普希茨控制的可训练去噪器已成为收敛图像重建的核心。然而，同时具备强去噪能力与全局利普希茨保证的神经网络训练极具挑战。现有方法仅经验性地施加利普希茨约束，无法提供超出训练数据的保证。本文通过利用图像网格上的置换作用，构建了一种全局非扩张（利普希茨界 ≤1）的神经架构。将该去噪器与前向成像算子结合，形成可证明为压缩的重建机制，从而实现全局收敛。在超分辨率、去模糊等标准逆问题上的实验表明，本方法性能与软约束基线相当，且提供严格利普希茨保证。
原文摘要 · Abstract (English)
Trainable denoisers with Lipschitz control have become central to convergent image reconstruction. However, training neural networks that simultaneously offer strong denoising performance and global Lipschitz guarantees is challenging. Existing approaches enforce Lipschitz control only empirically, providing no guarantees beyond the training data. In this work, we show that by exploiting the action of permutations on the image lattice, we can constrain a neural architecture that is globally nonexpansive (Lipschitz bound $\leqslant 1$). We integrate the proposed denoiser with forward imaging operators to develop a reconstruction mechanism that is provably contractive and therefore globally convergent. Experiments on standard inverse problems, such as superresolution and deblurring, demonstrate that our reconstruction performance is competitive with softly constrained baselines while providing Lipschitz guarantees.
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