论文标题
三线上的顶点的圆锥形ron换
The conical Radon transform with vertices on triple lines
论文作者
论文摘要
我们研究了圆锥体ra的反转，该反转从圆形锥体上的积分中整合了三维空间中的功能。由于其在各种成像应用中的相关性，例如康普顿相机成像和单个散射光学层析成像，因此最近引起了锥形ra。不受限制的锥形ra变换被过度确定，因为所有锥体的歧管都取决于六个变量：中心位置，轴向方向和锥体的开头。在这项工作中，我们考虑使用三线传感器的特定限制转换，其中收集了一组三维锥体上的积分，该积分由一维顶点集，一维中心轴和一维开口角度确定。作为本文的主要结果，我们得出了一个分析反转公式，用于受限的锥形ra transform。这样一来，我们定义了一个适合三线传感器的射线变换，我们为其建立一个分析反演公式。
We study the inversion of the conical Radon which integrates a function in three-dimensional space from integrals over circular cones. The conical Radon recently got significant attention due to its relevance in various imaging applications such as Compton camera imaging and single scattering optical tomography. The unrestricted conical Radon transform is over-determined because the manifold of all cones depends on six variables: the center position, the axis orientation and the opening angle of the cone. In this work, we consider a particular restricted transform using triple line sensors where integrals over a three-dimensional set of cones are collected, determined by a one-dimensional vertex set, a one-dimensional set of central axes, and the one-dimensional set of opening angle. As the main result in this paper, we derive an analytic inversion formula for the restricted conical Radon transform. Along that way we define a certain ray transform adapted to the triple line sensor for which we establish an analytic inversion formula.
