The X-Ray Transform on a Generic Family of Smooth Curves

被引：2

作者：

Zhang, Yang ^{[1
]}

机构：

[1] Univ Washington, Univ Washington Seattle Campus, Seattle, WA 98195 USA

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2023年 / 33卷 / 06期

关键词：

X-ray transform; A generic family of smooth curves; Conjugate points; Artifacts; GEOMETRY;

D O I：

10.1007/s12220-023-01236-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the X-ray transform over a generic family of smooth curves in 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.

引用

页数：27

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