Imaging based on Compton scattering: model-uncertainty and data-driven reconstruction methods

TL;DR

This paper explores Compton scattering tomography (CST), addressing inverse problem challenges like non-linearity and noise, by developing data-driven reconstruction algorithms that incorporate model uncertainty, validated through Monte Carlo simulations.

Contribution

It introduces two novel reconstruction algorithms for CST that handle model inexactness using a regularized subspace method and deep image prior, with theoretical and empirical validation.

Findings

RESESOP method is well-posed and regularizes the inverse problem.

Deep image prior effectively incorporates model uncertainty.

Algorithms perform well on Monte Carlo simulated data.

Abstract

The recent development of scintillation crystals combined with $\gamma$-rays sources opens the way to an imaging concept based on Compton scattering, namely Compton scattering tomography (CST). The associated inverse problem rises many challenges: non-linearity, multiple order-scattering and high level of noise. Already studied in the literature, these challenges lead unavoidably to uncertainty of the forward model. This work proposes to study exact and approximated forward models and develops two data-driven reconstruction algorithms able to tackle the inexactness of the forward model. The first one is based on the projective method called regularized sequential subspace optimization (RESESOP). We consider here a finite dimensional restriction of the semi-discrete forward model and show its well-posedness and regularisation properties. The second one considers the unsupervised learning method, deep image prior (DIP), inspired by the construction of the model uncertainty in RESESOP. The methods are validated on Monte-Carlo data.