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New Formulas for the Inversion of the Radon Transform Full article

Journal Doklady Mathematics
ISSN: 1064-5624 , E-ISSN: 1531-8362
Output data Year: 2025, Volume: 111, Number: 3, Pages: 163-166 Pages count : 4 DOI: 10.1134/s1064562425700139
Tags Radon transform, inversion formulas, integral geometry, probing, tomography, differential equation, discontinuous functions
Authors Anikonov D.S. 1 , Konovalova D.S. 1
Affiliations
1 Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

Funding (1)

1 Sobolev Institute of Mathematics FWNF-2022-0009

Abstract: Classical inversion formulas for the integral Radon transform assume that the integrand is smooth. However, this restriction does not fully correspond to application of results in probing theory, which is the main area of application of the Radon transform. It would be more natural to assume that jump discontinuities are admissible for integrands. The paper presents several inversion formulas proved by the authors for piecewise continuous functions. The formulas are compared, and preliminary recommendations on their use for numerical algorithms are given.
Cite: Anikonov D.S. , Konovalova D.S.
New Formulas for the Inversion of the Radon Transform
Doklady Mathematics. 2025. V.111. N3. P.163-166. DOI: 10.1134/s1064562425700139 WOS Scopus OpenAlex
Original: Аниконов Д.С. , Коновалова Д.С.
Новые формулы обращения преобразования Радона
Доклады Академии наук. Серия: Математика, информатика, процессы управления. 2025. Т.523. №1. С.11-14. DOI: 10.31857/S2686954325030027 РИНЦ
Dates:
Submitted: May 12, 2025
Accepted: May 29, 2025
Published print: Dec 9, 2025
Published online: Dec 9, 2025
Identifiers:
Web of science: WOS:001635416500011
Scopus: 2-s2.0-105024527255
OpenAlex: W4417162868
Citing: Пока нет цитирований
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