论文标题
在带有固定源的三维康普顿散射断层扫描系统上
On a three dimensional Compton scattering tomography system with fixed source
论文作者
论文摘要
康普顿散射层析成像是一种新兴技术，在非破坏性测试和医学扫描等成像中具有有吸引力的应用。在本文中，我们在三个维度上引入了一种新型的模式，并带有固定源和一个在球形表面上移动的单个检测器。我们还研究了ra transwort建模的模型，该数据由曲折表面上的积分组成。使用球形谐波，我们到达了将数据扩展系数与函数相关的广义ABEL S型方程。我们展示了其解决方案的独特性以及曲曲面ra transform的可逆性。我们使用Tikhonov正则化通过三个维度的数值重建来说明这一点。公共代码存储库中提供了用于离散球形谐波扩展的算法的初步版本。
Compton scatter tomography is an emerging technique with attractive applications in several fields in imaging such as non-destructive testing and medical scanning. In this paper, we introduce a novel modality in three dimensions with a fixed source and a single detector that moves on a spherical surface. We also study the Radon transform modeling the data that consists in 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 Tikhonov regularization. A preliminary version of the algorithm for discrete spherical harmonic expansion is available in a public code repository.
