A numerical solution of the dynamic vector tomography problem using the truncated singular value decomposition method

被引：2
|
作者：
Polyakova, Anna P. [1 ]
Svetov, Ivan E. [1 ]
机构：
[1] Sobolev Inst Math, Lab Ill Posed Proc, Novosibirsk, Russia
来源：
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS | 2024年 / 32卷 / 01期
关键词：
Dynamic vector tomography; longitudinal ray transform; transverse ray transform; singular value decomposition; orthogonal polynomial; FIELD TOMOGRAPHY; RADON-TRANSFORM; RAY TRANSFORMS; RECONSTRUCTION; INVERSION; COMPENSATION; PART;
D O I：
10.1515/jiip-2022-0019
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a problem of dynamic 2D vector tomography, i.e. the object under investigation changes during the data acquisition. More precisely, we consider the case when the object motion is a combination of rotation and shifting. The task is then to reconstruct the searched-for vector field by known values of the dynamic ray transforms. In order to solve this dynamic inverse problem, we first study properties of the dynamic ray transforms operators. In particular, the singular value decompositions of the operators are constructed using classic orthogonal polynomials. Following from this study, a numerical algorithm for solving the dynamic problem is proposed based on the truncated singular value decomposition method.
引用
收藏
页码：145 / 160
页数：16
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