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.

康普顿散射断层扫描是一种新兴的扫描技术，在无损检测和医学成像等多个领域具有有吸引力的应用。在本文中，我们研究了一种采用固定源和在球面上移动的单个探测器的三个维度的模态。我们还研究了对由复曲面上的积分组成的数据进行建模的 Radon 变换。使用球谐函数，我们可以得到一个广义的阿贝尔类型方程，该方程将数据的展开系数与函数的系数连接起来。我们展示了其解的唯一性以及复曲面 Radon 变换的可逆性。我们通过使用正则化方法在三个维度上进行数值重建来说明这一点。