Computed tomography image reconstruction from only two projections

TL;DR

This paper explores the ill-posed problem of reconstructing CT images from only two projections, demonstrating that classical methods fail and proposing Bayesian Markov modeling as a potential solution, supported by Matlab demonstrations.

Contribution

It introduces a Bayesian Markov modeling approach for CT image reconstruction from minimal projections, highlighting its potential over traditional methods.

Findings

Classical methods are inadequate for two-projection CT reconstruction.

Bayesian Markov modeling offers a promising alternative.

Matlab programs demonstrate the proposed approach.

Abstract

English: This paper concerns the image reconstruction from a few projections in Computed Tomography (CT). The main objective of this paper is to show that the problem is so ill posed that no classical method, such as analytical methods based on inverse Radon transform, nor the algebraic methods such as Least squares (LS) or regularization theory can give satisfactory result. As an example, we consider in detail the case of image reconstruction from two horizontal and vertical projections. We then show how a particular composite Markov modeling and the Bayesian estimation framework can possibly propose satisfactory solutions to the problem. For demonstration and educational purpose a set of Matlab programs are given for a live presentation of the results. ----- French: Ce travail, \`a but p\'edagogique, pr\'esente le probl\`eme inverse de la reconstruction d'image en tomographie X lorsque le nombre des projections est tr\`es limit\'e. voir le texte en Anglais et en Fran\c{c}ais.