论文标题
从Neumann Traces恢复波方程的初始数据
Recovering the Initial Data of the Wave Equation from Neumann Traces
论文作者
论文摘要
我们研究了从任意空间尺寸以凸域边界上的溶液的Neumann Trace（正常导数）中恢复标准波方程的初始数据（F，0）的问题。除其他外，此问题与包括光声断层扫描在内的层析成像图像重建有关。我们建立了反向投影类型的显式反转公式，该公式将初始数据恢复到平滑积分运算符定义的加性项。在域的边界是椭圆形的情况下，积分操作员消失了，因此我们获得了一个分析公式，用于从椭圆形的波方程的neumann痕迹中恢复初始数据。
We study the problem of recovering the initial data (f, 0) of the standard wave equation from the Neumann trace (the normal derivative) of the solution on the boundary of convex domains in arbitrary spatial dimension. Among others, this problem is relevant for tomographic image reconstruction including photoacoustic tomography. We establish explicit inversion formulas of the back-projection type that recover the initial data up to an additive term defined by a smoothing integral operator. In the case that the boundary of the domain is an ellipsoid, the integral operator vanishes, and hence we obtain an analytic formula for recovering the initial data from Neumann traces of the wave equation on ellipsoids.
