A Reconstruction Approach for Imaging in 3D Cone Beam Vector Field Tomography
A Reconstruction Approach for Imaging in 3D Cone Beam Vector Field Tomography
复制标题
3D 锥形束矢量场断层扫描成像重建方法
DOI：
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发表时间：
2009
影响因子：
7.6
通讯作者：
A. Louis
中科院分区：
文献类型：
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作者：
T. Schuster;D. Theis;A. Louis
三维锥束矢量场层析成像（VFT）的目的是通过测量矢量场投影的线积分来重建和可视化运动流体的速度场。通过沿围绕对象的扫描曲线沿着进行超声测量来获得数据。从数学的观点来看，我们必须处理矢量锥束变换的反演问题。由于任何具有紧支集的梯度向量场的向量锥束变换恒等于零，我们只能希望重建任意向量场的螺线管部分。本文首先总结了三维螺线管矢量场锥束变换的重要性质，然后提出了一种基于近似逆的求解方法。在这种情况下，我们集中利用标量三维计算机断层扫描的结果。本文中提出的研究结果将继续说明从第一个数值实验的图片完成准确的，模拟数据。
3D cone beam vector field tomography (VFT) aims for reconstructing and visualizing the velocity field of a moving fluid by measuring line integrals of projections of the vector field. The data are obtained by ultrasound measurements along a scanning curve which surrounds the object. From a mathematical point of view, we have to deal with the inversion of the vectorial cone beam transform. Since the vectorial cone beam transform of any gradient vector field with compact support is identically equal to zero, we can only hope to reconstruct the solenoidal part of an arbitrary vector field. In this paper we will at first summarize important properties of the cone beam transform for three-dimensional solenoidal vector fields and then propose a solution approach based on the method of approximate inverse. In this context, we intensively make use of results from scalar 3D computerized tomography. The findings presented in the paper will continuously be illustrated by pictures from first numerical experiments done with exact, simulated data.