Inversion of the star transform
Inversion of the star transform
复制标题
星形变换的反转
DOI：
10.1088/0266-5611/30/10/105001
复制
发表时间：
2014
期刊：
影响因子：
2.1
通讯作者：
Vadim A. Markel
中科院分区：
文献类型：
--
作者：
Fan Zhao;J. Schotland;Vadim A. Markel
我们将星形变换定义为我们在之前的工作中引入的破碎射线变换的推广。使用星形变换的优点包括可以单独且同时（根据相同的数据）重建介质的吸收和散射系数，以及可以利用在传统 X 射线断层扫描的情况下被丢弃的散射辐射。本文从物理原理出发推导了星形变换，讨论了其数学性质并分析了反演的数值稳定性。特别地，表明只有对于涉及奇数条射线的配置才能获得星形变换的稳定反演。推导了几种计算效率高的反演算法并进行了数值测试。
We define the star transform as a generalization of the broken ray transform introduced by us in previous work. The advantages of using the star transform include the possibility to reconstruct the absorption and the scattering coefficients of the medium separately and simultaneously (from the same data) and the possibility to utilize scattered radiation which, in the case of conventional x-ray tomography, is discarded. In this paper, we derive the star transform from physical principles, discuss its mathematical properties and analyze numerical stability of inversion. In particular, it is shown that stable inversion of the star transform can be obtained only for configurations involving odd number of rays. Several computationally-efficient inversion algorithms are derived and tested numerically.
单散射光学断层扫描：同时重建散射和吸收。
DOI：
10.1103/physreve.81.016602
发表时间：
2010
期刊：
Physical review. E, Statistical, nonlinear, and soft matter physics
影响因子：
--
作者：
Florescu,Lucia;Markel,VadimA;Schotland,JohnC
通讯作者：
Schotland,JohnC