论文标题
通过在两个几何设置中测量的分数波方程解的初始函数重建初始函数
Reconstruction of the initial function from the solution of the fractional wave equation measured in two geometric settings
论文作者
论文摘要
光声断层扫描（PAT）是基于医学成像领域的一种新颖且迅速的技术，基于通过刺激非电离激光脉冲在感兴趣的对象内的声波产生。使用对象外部的检测器测量这种声波，并通过多个反转转换为人体的图像。因此，PAT中的数学问题之一是如何从对象外部的波方程解中恢复初始函数。在这项研究中，我们考虑了分数波方程，并假设点状检测器位于球体和超平面上。我们提供了如何从数据中恢复初始函数，即在球体和超平面上测量的分数波方程的解。
Photoacoustic tomography (PAT) is a novel and rapidly promising technique in the field of medical imaging, based on the generation of acoustic waves inside an object of interest by stimulating non-ionizing laser pulses. This acoustic wave is measured using the detector on the outside of the object and converted into an image of the human body by several inversions. Thus, one of mathematical problems in PAT is how to recover the initial function from the solution of the wave equation on the outside of the object. In this study we consider the fractional wave equation and assume that the point-like detectors are located on the sphere and hyperplane. We provide how to recover the initial function from the data, the solution of the fractional wave equation, measured on the sphere and hyperplane.
