发表机构
Indian Institute of Science（印度科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究如何训练用于图像重建的去噪器，利用排列对图像格的作用约束神经架构，使其全局非扩张，集成去噪器与成像算子开发出可证明收缩且全局收敛的重建机制，实验表明性能有竞争力且提供Lipschitz保证。
AI 中文摘要
具有Lipschitz控制的可训练去噪器已成为收敛图像重建的核心。然而，训练同时具有强大去噪性能和全局Lipschitz保证的神经网络具有挑战性。现有方法仅凭经验实施Lipschitz控制，除训练数据外无保证。本文表明，通过利用排列在图像格上的作用，可约束全局非扩张（Lipschitz界≤1）的神经架构。将其与前向成像算子集成开发出可证明收缩且全局收敛的重建机制。在超分辨率和去模糊等标准逆问题上的实验表明，我们的重建性能与软约束基线竞争且提供Lipschitz保证。
英文摘要
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.
Commentsaccepted at ICML 2026
