Three dimensional Compton scattering tomography
Three dimensional Compton scattering tomography
复制标题
三维康普顿散射断层扫描
DOI：
10.1088/1361-6420/aac51e
复制
发表时间：
2017
期刊：
影响因子：
2.1
通讯作者：
W. Lionheart
中科院分区：
文献类型：
--
作者：
James W. Webber;W. Lionheart
我们提出了一种新的获取几何形状的电子密度重建在三维x射线康普顿成像使用单色源。这将我们引向一个新的三维逆问题，我们的目标是从主轴环面上的积分重建一个实值函数f（电子密度）。证明了空心球紧支光滑函数集上广义主轴环面变换的注入性。这是通过对一类Volterra积分算子的显式反演得到的，它的解给出了f的调和系数的表达式。随后考虑了多色源的情况，证明了一种新的主轴内变换、苹果变换和苹果内变换在紧支撑在空心球上的光滑函数集上的注入性。对这两种源类型提出了一种可能的物理模型。我们还提供了不同程度的伪随机噪声的模拟密度重建，并在我们的模拟中模拟了由于入射和散射射线衰减引起的系统误差。
We propose a new acquisition geometry for electron density reconstruction in three dimensional x-ray Compton imaging using a monochromatic source. This leads us to a new three dimensional inverse problem where we aim to reconstruct a real valued function f (the electron density) from its integrals over spindle tori. We prove injectivity of a generalized spindle torus transform on the set of smooth functions compactly supported on a hollow ball. This is obtained through the explicit inversion of a class of Volterra integral operators, whose solutions give us an expression for the harmonic coefficients of f. The polychromatic source case is later considered, and we prove injectivity of a new spindle interior transform, apple transform and apple interior transform on the set of smooth functions compactly supported on a hollow ball. A possible physical model is suggested for both source types. We also provide simulated density reconstructions with varying levels of added pseudo random noise and model the systematic error due to the attenuation of the incoming and scattered rays in our simulation.