论文标题
X射线转换在普通曲线的通用家族上
The X-ray transform on a generic family of smooth curves
论文作者
论文摘要
我们研究了$ \ mathbb {r}^2 $的普通曲线的X射线转换，并带有Riemannian Metric $ g $。我们表明，在存在共轭点的情况下，无法从局部数据中回收奇点，因此在重建中可能会产生伪影。我们执行数值实验以说明结果。
We study the X-ray transform over a generic family of smooth curves in $\mathbb{R}^2$ with a Riemannian metric $g$. We show that the singularities cannot be recovered from local data in the presence of conjugate points, and therefore artifacts may arise in the reconstruction. We perform numerical experiments to illustrate the results.
