RECONSTRUCTION OF A FUNCTION AND ITS SINGULAR SUPPORT IN A CYLINDER BY TOMOGRAPHIC DATA

被引：3
作者：
Maltseva, S., V [1 ]
Svetov, I. E. [1 ]
Polyakova, A. P. [1 ]
机构：
[1] Sobolev Inst Math, Novosibirsk 630090, Russia
来源：
EURASIAN JOURNAL OF MATHEMATICAL AND COMPUTER APPLICATIONS | 2020年 / 8卷 / 02期
关键词：
tomography; refraction; absorption; attenuated geodesic x-ray transform; Riemannian metric; singular support; RAY TRANSFORM; VECTOR-FIELDS; INVERSION;
D O I：
10.32523/2306-6172-2020-8-2-86-97
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article we consider problems of reconstruction of a function and its singular support by using tomographic data. The data for the problems are values of the attenuated geodesic x-ray transform which is a set of integrals of an unknown function calculated along geodesics of the Riemannian metric that is used for modelling refraction in a cylinder. The values of the attenuated geodesic x-ray transform are received in a slice-by-slice fan-beam scheme. Our approach is based on the slice-by-slice reconstruction of the sought-for function or its singular support using a modification of well-known operators of back-projection and break indicator.
引用
收藏
页码：86 / 97
页数：12
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