Learning-based approaches for reconstructions with inexact operators in nanoCT applications

TL;DR

This paper compares traditional and learned reconstruction methods for nanoCT imaging when the forward model is inaccurate, highlighting the potential of neural networks for improved results and uncertainty quantification.

Contribution

It introduces and evaluates learned reconstruction schemes, including U-Nets and invertible neural networks, for inexact forward operators in nanoCT imaging.

Findings

Learned methods outperform traditional iterative approaches in inexact settings.

Invertible neural networks enable uncertainty quantification.

Extensive experiments demonstrate the effectiveness of proposed methods.

Abstract

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.