ABSTRACT Compton-scattering tomography is an imaging technique that exploits the energy dependence of Compton-scattered radiation. This image reconstruction problem is characterized by measurements of path integrals over circular arcs. In the conventional x-ray transmission computed tomography (CT) problem, the path integrals are along straight lines. We show that, with a simple transformation of variables, the circular-arc problem can be expressed as the filtered-backprojection solution identical to that of the straight-line CT problem.

中文翻译：

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具有一个源和一个探测器的康普顿散射断层扫描：滤波反投影解决方案的简单推导

摘要 康普顿散射断层扫描是一种利用康普顿散射辐射的能量依赖性的成像技术。这个图像重建问题的特点是测量圆弧上的路径积分。在传统的 X 射线透射计算机断层扫描 (CT) 问题中，路径积分是沿着直线进行的。我们表明，通过简单的变量转换，圆弧问题可以表示为与直线 CT 问题相同的滤波反投影解决方案。