Exact inversion of an integral transform arising in Compton camera imaging
Exact inversion of an integral transform arising in Compton camera imaging
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康普顿相机成像中积分变换的精确反演
DOI：
10.1117/1.jmi.7.3.032504
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发表时间：
2020
影响因子：
2.4
通讯作者：
F. Terzioglu
中科院分区：
文献类型：
--
作者：
F. Terzioglu
抽象的。目的：该文件地址的积分变换，称为康普顿（或锥）变换，映射一个三维（3-D）的功能，其在R3的圆锥表面积分的精确反演。康普顿变换是在康普顿照相机对γ射线源的被动探测中提出的，它在医学、工业成像、国土安全成像和天文学等领域有着广阔的应用前景。方法：一个广义的身份关系的康普顿和氡变换制定。建议的关系可以用来设计一种方法，用于转换的康普顿变换数据的函数到其Radon投影。然后可以使用用于Radon变换的众所周知的反演技术来恢复该函数。结果如下：我们推导了一个两步方法，使用完整的可用投影集来反演康普顿变换：首先，从康普顿变换恢复Radon变换，然后Radon变换反演。所提出的技术是独立的检测器的几何形状，只要满足一个慷慨的容许条件。结论：提出了三维康普顿变换的精确反演公式.通过数值模拟证明了该反演算法的稳定性。
Abstract. Purpose: The paper addresses exact inversion of the integral transform, called the Compton (or cone) transform, that maps a three-dimensional (3-D) function to its integrals over conical surfaces in R3. Compton transform arises in passive detection of gamma-ray sources with a Compton camera, which has promising applications in medical and industrial imaging as well as in homeland security imaging and astronomy. Approach: A generalized identity relating the Compton and the Radon transforms was formulated. The proposed relation can be used to devise a method for converting the Compton transform data of a function into its Radon projections. The function can then be recovered using well-known inversion techniques for the Radon transform. Results: We derived a two-step method that uses the full set of available projections to invert the Compton transform: first, the recovery of the Radon transform from the Compton transform, and then the Radon transform inversion. The proposed technique is independent of the geometry of detectors as long as a generous admissibility condition is met. Conclusions: We proposed an exact inversion formula for the 3-D Compton transform. The stability of the inversion algorithm was demonstrated via numerical simulations.
康普顿相机成像和锥体变换：简要概述
影响因子：
2.1
作者：
Terzioglu, Fatma;Kuchment, Peter;Kunyansky, Leonid
通讯作者：
Kunyansky, Leonid