Tomography: mathematical aspects and applications

TL;DR

This paper reviews the Radon transform and explores new mathematical results in tomography through a variational approach, offering insights into reconstruction stability and potential generalizations.

Contribution

It introduces a novel variational formulation for tomography based on a Mumford-Shah type functional, advancing mathematical understanding and reconstruction techniques.

Findings

New mathematical results on tomography stability

A variational reconstruction method using Mumford-Shah functional

Discussion of physical interpretation and potential generalizations

Abstract

In this article we present a review of the Radon transform and the instability of the tomographic reconstruction process. We show some new mathematical results in tomography obtained by a variational formulation of the reconstruction problem based on the minimization of a Mumford-Shah type functional. Finally, we exhibit a physical interpretation of this new technique and discuss some possible generalizations.