PDE-based numerical method for a limited angle X-ray tomography

TL;DR

This paper introduces a PDE-based numerical approach for limited angle X-ray tomography, utilizing the transport PDE and quasi-reversibility, with convergence analysis and numerical validation against traditional methods.

Contribution

It presents a novel PDE-based method for incomplete Radon data in X-ray tomography, including convergence analysis and applications to attenuated transforms.

Findings

The method effectively reconstructs images from limited angle data.

Convergence is proven using a new Carleman estimate.

Numerical results compare favorably with filtered back projection.

Abstract

A new numerical method for X-ray tomography for a specific case of incomplete Radon data is proposed. Potential applications are in checking out bulky luggage in airports. This method is based on the analysis of the transport PDE governing the X-ray tomography rather than on the conventional integral formulation. The quasi-reversibility method is applied. Convergence analysis is performed using a new Carleman estimate. Numerical results are presented and compared with the inversion of the Radon transform using the well-known filtered back projection algorithm. In addition, it is shown how to use our method to study the inversion of the attenuated X-ray transform for the same case of incomplete data.