  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.
