用截断奇异值分解方法求解动态矢量层析成像问题

IF 0.9 4区数学 Q2 MATHEMATICS

Journal of Inverse and Ill-Posed Problems Pub Date : 2022-10-25 DOI:10.1515/jiip-2022-0019

A. Polyakova, I. Svetov

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引用次数: 1

摘要

摘要我们考虑了动态二维矢量层析成像的一个问题，即在数据采集过程中，被调查对象会发生变化。更准确地说，我们考虑的情况是，物体运动是旋转和移动的结合。然后，任务是通过动态射线变换的已知值来重建搜索到的矢量场。为了解决这个动态逆问题，我们首先研究了动态射线变换算子的性质。特别地，算子的奇异值分解是使用经典的正交多项式构造的。在此基础上，基于截断奇异值分解方法，提出了一种求解动态问题的数值算法。

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

Abstract 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.

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来源期刊

Journal of Inverse and Ill-Posed Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： This journal aims to present original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published. Issues of the Journal of Inverse and Ill-Posed Problems contain high quality papers which have an innovative approach and topical interest. The following topics are covered: Inverse problems existence and uniqueness theorems stability estimates optimization and identification problems numerical methods Ill-posed problems regularization theory operator equations integral geometry Applications inverse problems in geophysics, electrodynamics and acoustics inverse problems in ecology inverse and ill-posed problems in medicine mathematical problems of tomography