发表机构
University of Siegen; Helmholtz Imaging; Deutsches Elektronen-Synchrotron DESY; Universität Hamburg（锡根大学; 亥姆霍兹成像研究所; 德国电子同步加速器研究所; 汉堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究从神经算子视角分析逆成像问题的U-Net架构，对比不同神经算子U-Net的优缺点，发现经典U-Net对分辨率变化的鲁棒性优于天生分辨率不变的U型神经算子架构。
AI 中文摘要
深度神经网络在解决各类不适定成像逆问题上已取得显著的经验成功。然而，极少有研究关注当离散化的病态问题转变为真正不适定问题（即离散化分辨率不断提高）时神经网络的表现。本研究回顾了类U-Net架构中神经算子学习的常用方法，U-Net是逆成像问题中最常用的经典架构之一。我们讨论了各方法的优缺点，考虑了一个1D示例以提升可解释性，并针对不同类型的神经算子U-Net如何改善初步（粗糙）有限角度CT重建开展了大量数值实验。特别地，我们研究了针对某一离散化分辨率训练的网络对其他分辨率的泛化能力。我们的发现是，尽管U型神经算子架构天生具有分辨率不变性，但经典U-Net架构对分辨率变化的鲁棒性似乎超出预期。
英文摘要
Deep neural networks have shown great empirical success in the solution of a wide variety of ill-posed inverse problems in imaging. Yet, very few works have studied their behavior in the limit that turns the discretized ill-conditioned problems into truly ill-posed ones, i.e., for an increasing resolution of the discretization. In this work, we review common approaches to neural operator learning in architectures that resemble a U-Net, one of the most common classical architectures for inverse imaging problems. We discuss advantages and drawbacks of the respective approaches, consider a 1D toy example for improved interpretability, and present extensive numerical experiments on how different types of neural operator U-Nets can improve a first (crude) limited angle CT-reconstruction. In particular, we study how well networks trained for a certain resolution of the discretization generalize to other resolutions. Our finding is that while U-shaped neural operator architectures are by design resolution-invariant, the classical U-Net architecture seems to be more robust with respect to resolution changes than expected.
