论文标题
用于解决反问题的学习NetT正规化的离散化
Discretization of learned NETT regularization for solving inverse problems
论文作者
论文摘要
基于深度学习的重建方法为解决反问题提供了出色的结果，因此变得越来越重要。最近发明的基于学习的重建方法是所谓的NetT（用于网络Tikhonov正则化），该方法包含训练有素的神经网络，作为广义Tikhonov正则化的正常化器。 NETT的现有分析考虑了固定的操作员和固定的正规化程序，并将收敛性分析，因为数据中的噪声水平接近零。在本文中，我们大大扩展了框架和分析，以反映各种实际方面，并考虑到数据空间，解决方案空间，向前操作员和定义正常化程序的神经网络的离散化。我们显示了离散化NETT方法的渐近收敛性，以降低噪声水平和离散误差。此外，我们得出了收敛速率，并为光声断层扫描中有限的数据问题提供了数值结果。
Deep learning based reconstruction methods deliver outstanding results for solving inverse problems and are therefore becoming increasingly important. A recently invented class of learning-based reconstruction methods is the so-called NETT (for Network Tikhonov Regularization), which contains a trained neural network as regularizer in generalized Tikhonov regularization. The existing analysis of NETT considers fixed operator and fixed regularizer and analyzes the convergence as the noise level in the data approaches zero. In this paper, we extend the frameworks and analysis considerably to reflect various practical aspects and take into account discretization of the data space, the solution space, the forward operator and the neural network defining the regularizer. We show the asymptotic convergence of the discretized NETT approach for decreasing noise levels and discretization errors. Additionally, we derive convergence rates and present numerical results for a limited data problem in photoacoustic tomography.
