基于法线、纵向和加权拉顿变换值的三维矢量场重构

IF 0.58 Q3 Engineering

Journal of Applied and Industrial Mathematics Pub Date : 2024-02-16 DOI:10.1134/S1990478923040130

I. E. Svetov, A. P. Polyakova

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引用次数: 0

摘要

摘要本文考虑了根据非加权（法线和纵向）和加权 Radon 变换的值重建三维向量场的向量断层成像问题。利用文中获得的矢量场详细分解，建立了作用于矢量场的非加权和加权 Radon 变换与作用于函数的 Radon 变换之间的联系。特别是描述了作用于向量场的断层扫描积分算子的核。文中还考虑了矢量场重建的一些层析问题，并获得了这些问题的反演求解公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Reconstruction of Three-Dimensional Vector Fields Based on Values of Normal, Longitudinal, and Weighted Radon Transforms

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.

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来源期刊

Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering

CiteScore

1.00

自引率

0.00%

发文量

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.