关于锥形Radon变换的精确重建公式
Exact reconstruction formulas for a Radon transform over cones
AI总结：
本文研究了考虑康普顿散射的锥形Radon变换，推导出一种滤波反投影类型的精确重建公式，用于逆变换。
摘要：
Radon变换的逆变换是许多现代断层成像技术的数学基础。本文研究了锥形Radon变换，这对于考虑康普顿散射的计算机断层摄影术至关重要。所研究的锥形Radon变换将$\R^d$中的函数积分到所有顶点位于超平面且对称轴垂直于该平面的锥形表面。我们的主要结果是推导出一种滤波反投影类型的精确重建公式，用于逆变换此变换。
英文摘要：
Inversion of Radon transforms is the mathematical foundation of many modern tomographic imaging modalities. In this paper we study a conical Radon transform, which is important for computed tomography taking Compton scattering into account. The conical Radon transform we study integrates a function in $\R^d$ over all conical surfaces having vertices on a hyperplane and symmetry axis orthogonal to this plane. As the main result we derive exact reconstruction formulas of the filtered back-projection type for inverting this transform.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
