{"title":"Reconstruction of Parameters of a Set of Radiant Points from Their Images","authors":"E. Yu. Derevtsov","doi":"10.1134/s1055134423040028","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Within the framework of geometric tomography, inverse problems of photometry, wave\noptics, and discrete tomography, we study questions on reconstruction of the spatial location and\nluminosity of a discrete distribution of radiant sources from its images obtained with the use of\na small number of optical systems. We analyze the problem on finding geometric parameters of\nsuch a distribution and describe sources of ambiguity. We consider the inverse problem on\nreconstruction of a discrete distribution that consists of incoherent and monochromatic sources\nand suggest uniqueness criteria for its solution. We also suggest a constructive approach to\nnumerical solution of the inverse problem on reconstruction of the coordinates and luminosity of\na family of radiant pinpoint sources from their images.\n</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":"15 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siberian Advances in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1055134423040028","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Within the framework of geometric tomography, inverse problems of photometry, wave
optics, and discrete tomography, we study questions on reconstruction of the spatial location and
luminosity of a discrete distribution of radiant sources from its images obtained with the use of
a small number of optical systems. We analyze the problem on finding geometric parameters of
such a distribution and describe sources of ambiguity. We consider the inverse problem on
reconstruction of a discrete distribution that consists of incoherent and monochromatic sources
and suggest uniqueness criteria for its solution. We also suggest a constructive approach to
numerical solution of the inverse problem on reconstruction of the coordinates and luminosity of
a family of radiant pinpoint sources from their images.
期刊介绍：
Siberian Advances in Mathematics is a journal that publishes articles on fundamental and applied mathematics. It covers a broad spectrum of subjects: algebra and logic, real and complex analysis, functional analysis, differential equations, mathematical physics, geometry and topology, probability and mathematical statistics, mathematical cybernetics, mathematical economics, mathematical problems of geophysics and tomography, numerical methods, and optimization theory.
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