Imaging problems such as the one in nanoCT require the solution of an inverse problem, where it is often taken for granted that the forward operator, i.e., the underlying physical model, is properly known. In the present work we address the problem where the forward model is inexact due to stochastic or deterministic deviations during the measurement process. We particularly investigate the performance of non-learned iterative reconstruction methods dealing with inexactness and learned reconstruction schemes, which are based on U-Nets and conditional invertible neural networks. The latter also provide the opportunity for uncertainty quantification. A synthetic large data set in line with a typical nanoCT setting is provided and extensive numerical experiments are conducted evaluating the proposed methods.

翻译：成像问题（如纳米CT成像）需要求解逆问题，这类问题通常默认正向算子（即底层物理模型）被精确已知。然而，本研究针对测量过程中因随机或确定性偏差导致正向模型不精确的问题展开探讨。我们特别研究了应对非精确性的非学习型迭代重建方法，以及基于U-Net和条件可逆神经网络的学习型重建方案——后者还可实现不确定性量化。本文提供了符合典型纳米CT场景的合成大数据集，并通过大量数值实验对所提方法进行了系统评估。