{"title":"Reconstruction of Three-Dimensional Vector Fields Based on Values of Normal, Longitudinal, and Weighted Radon Transforms","authors":"I. E. Svetov, A. P. Polyakova","doi":"10.1134/S1990478923040130","DOIUrl":null,"url":null,"abstract":"<p> The paper considers the vector tomography problem of reconstructing a three-dimensional\nvector field based on the values of unweighted (normal and longitudinal) and weighted Radon\ntransforms. Using the detailed decomposition of vector fields obtained in the paper, connections\nare established between the unweighted and weighted Radon transforms acting on vector fields\nand the Radon transform acting on functions. In particular, the kernels of tomographic integral\noperators acting on vector fields are described. Some statements of tomography problems for the\nreconstruction of vector fields are considered, and inversion formulas for their solution are\nobtained.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 4","pages":"842 - 858"},"PeriodicalIF":0.5800,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478923040130","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
The paper considers the vector tomography problem of reconstructing a three-dimensional
vector field based on the values of unweighted (normal and longitudinal) and weighted Radon
transforms. Using the detailed decomposition of vector fields obtained in the paper, connections
are established between the unweighted and weighted Radon transforms acting on vector fields
and the Radon transform acting on functions. In particular, the kernels of tomographic integral
operators acting on vector fields are described. Some statements of tomography problems for the
reconstruction of vector fields are considered, and inversion formulas for their solution are
obtained.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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