An analytical reconstruction formula with efficient implementation for a modality of Compton Scattering Tomography with translational geometry

TL;DR

This paper introduces an efficient Fourier domain-based exact inversion formula for Compton Scattering Tomography with translational geometry, improving numerical stability and implementation over previous methods.

Contribution

It presents a new analytical reconstruction formula that simplifies implementation and enhances stability for Compton Scattering Tomography in translational geometry.

Findings

The proposed method is computationally efficient.

Simulations demonstrate improved stability and accuracy.

The Fourier domain approach simplifies the inversion process.

Abstract

In this paper, we address an alternative formulation for the exact inverse formula of the Radon transform on circle arcs arising in a modality of Compton Scattering Tomography in translational geometry proposed by Webber and Miller (Inverse Problems (36)2, 025007, 2020). The original study proposes a first method of reconstruction, using the theory of Volterra integral equations. The numerical realization of such a type of inverse formula may exhibit some difficulties, mainly due to stability issues. Here, we provide a suitable formulation for exact inversion that can be straightforwardly implemented in the Fourier domain. Simulations are carried out to illustrate the efficiency of the proposed reconstruction algorithm.