2021/11/20 by Tarpau, Cécilia, Cebeiro, Javier, Rollet, Geneviève +2
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2112.01632
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.