AN INVERSE PROBLEM FOR GENERALIZED RADON TRANSFORMATION [ОБРАТНАЯ ЗАДАЧА ДЛЯ ОБОБЩЕННОГО ПРЕОБРАЗОВАНИЯ РАДОНА] Full article
| Journal |
Научно-технические ведомости СПбГПУ. Физико-математические науки (ST PETERSBURG POLYTECHNIC UNIVERSITY JOURNAL-PHYSICS AND MATHEMATICS)
ISSN: 2304-9782 , E-ISSN: 2618-8686 |
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| Output data | Year: 2022, Volume: 15, Number: 1, Pages: 41-51 Pages count : 11 DOI: 10.18721/JPM.15104 | ||
| Tags | differential equation; discontinuous function; generalized Radon transformation; integral geometry | ||
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Abstract:
The paper studies the problem of inverting the integral transformation of Radon, whose formula, under traditional restrictions, gives the integrand values at any point. For the case when such a function is discontinuous and depends not only on the points of 3D space, but also on the parameters characterizing the plane of integration, these integrals have been named the generalized Radon transform (GRT). For the GRT inversion problem, the matching between quantities of known variables and variables of the integrand did not allow us to fully find the desired function. In this paper, only a part of this function was selected, namely, the discontinuity surface of the integrand for the GRT. An algorithm for solving the problem was put forward, and it was supported by a concrete example. © 2022 Editorial Committee of Tropical Geography
Cite:
Anikonov D.S.
, Balakina E.Y.
, Konovalova D.S.
AN INVERSE PROBLEM FOR GENERALIZED RADON TRANSFORMATION [ОБРАТНАЯ ЗАДАЧА ДЛЯ ОБОБЩЕННОГО ПРЕОБРАЗОВАНИЯ РАДОНА]
Научно-технические ведомости СПбГПУ. Физико-математические науки (ST PETERSBURG POLYTECHNIC UNIVERSITY JOURNAL-PHYSICS AND MATHEMATICS). 2022. V.15. N1. P.41-51. DOI: 10.18721/JPM.15104 WOS Scopus РИНЦ OpenAlex
AN INVERSE PROBLEM FOR GENERALIZED RADON TRANSFORMATION [ОБРАТНАЯ ЗАДАЧА ДЛЯ ОБОБЩЕННОГО ПРЕОБРАЗОВАНИЯ РАДОНА]
Научно-технические ведомости СПбГПУ. Физико-математические науки (ST PETERSBURG POLYTECHNIC UNIVERSITY JOURNAL-PHYSICS AND MATHEMATICS). 2022. V.15. N1. P.41-51. DOI: 10.18721/JPM.15104 WOS Scopus РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:000787998100004 |
| Scopus: | 2-s2.0-85132609283 |
| Elibrary: | 48235364 |
| OpenAlex: | W4385229053 |