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arXiv · 2112.01632

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

Cécilia Tarpau·Javier Cebeiro·Geneviève Rollet·Mai K. Nguyen·Laurent Dumas
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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.

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Cécilia Tarpau, Javier Cebeiro, Geneviève Rollet, Mai K. Nguyen, Laurent Dumas. 2021-11-20. An analytical reconstruction formula with efficient implementation for a modality of Compton Scattering Tomography with translational geometry. https://arxiv.org/abs/2112.01632

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