Analytical reconstruction formula with efficient implementation for a modality of Compton scattering tomography with translational geometry | Zendy

Cécilia Tarpau | Zendy; Javier Cebeiro | Zendy; G. Rollet | Zendy; Maï K. Nguyen | Zendy; Laurent Dumas | Zendy

Open Access

Analytical reconstruction formula with efficient implementation for a modality of Compton scattering tomography with translational geometry

Author(s) -

Cécilia Tarpau,

Javier Cebeiro,

G. Rollet,

Maï K. Nguyen,

Laurent Dumas

Publication year - 2021

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.

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