Learning-Based Approaches for Reconstructions With Inexact Operators in nanoCT Applications

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.