An analytical reconstruction formula with efficient implementation for a modality of Compton Scattering Tomography with translational geometry
Numerical Analysis
2021-12-06 v1 Numerical Analysis
Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2112.01632,
title = {An analytical reconstruction formula with efficient implementation for a modality of Compton Scattering Tomography with translational geometry},
author = {Cécilia Tarpau and Javier Cebeiro and Geneviève Rollet and Mai K. Nguyen and Laurent Dumas},
journal= {arXiv preprint arXiv:2112.01632},
year = {2021}
}
Comments
13 pages, 6 figures