Open AccessAnalytical reconstruction formula with efficient implementation for a modality of Compton scattering tomography with translational geometry
Author(s) -
Cécilia Tarpau,
Javier Cebeiro,
Geneviève Rollet,
Maï K. Nguyen,
Laurent Dumas
Publication year - 2022
Publication title -
inverse problems and imaging
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.755
H-Index - 40
eISSN - 1930-8345
pISSN - 1930-8337
DOI - 10.3934/ipi.2021075
Subject(s) - inverse problem , integral geometry , inverse , fourier transform , computer science , fourier domain , tomography , mathematics , algorithm , geometry , mathematical analysis , physics , optics
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.