On a three-dimensional Compton scattering tomography system with fixed source

Compton scattering tomography is an emerging scanning technique with attractive applications in several fields such as non-destructive testing and medical imaging. In this paper, we study a modality in three dimensions that employs a fixed source and a single detector moving on a spherical surface. We also study the Radon transform modeling the data that consists of integrals on toric surfaces. Using spherical harmonics we arrive to a generalized Abel’s type equation connecting the coefficients of the expansion of the data with those of the function. We show the uniqueness of its solution and so the invertibility of the toric Radon transform. We illustrate this through numerical reconstructions in three dimensions using a regularized approach.