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Sibirskii Zhurnal Industrial'noi Matematiki, 2020, Volume 23, Number 4, Pages 18–29
DOI: https://doi.org/10.33048/SIBJIM.2020.23.402 (Mi sjim1106) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On phase correction in tomographic research

Ya. Wanga, A. S. Leonovb, D. V. Lukyanenkoc, V. D. Shinkarevc, A. G. Yagolac

a Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, P. O. Box 9825, Beijing 100029, P. R. China
b Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, P.O. Box 9825, Beijing 100029, P.R. China
c National Research Nuclear University (MEPhI), Kashirskoye sh. 31, Moscow 115409, Russia
Full-text PDF (789 kB) Citations (3)
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DOI: https://doi.org/10.33048/SIBJIM.2020.23.402
Abstract: Under consideration is the problem of improving the contrast of the image obtained by processing tomographic projections with phase distortion. The study is based on the well-known intensity transfer equation. Unlike other works, this equation is solved in a bounded region of variation of the tomographic parameters. In a domain, a boundary value problem is posed for the intensity transfer equation which is then specialized for a three-dimensional parallel tomographic scheme. The case of two-dimensional tomography is also considered, together with the corresponding boundary value problem for the intensity transfer equation. We propose numerical methods for solving the boundary value problems of phase correction. The results are given of the numerical experiments on correction of tomographic projections and reconstruction of the structure of the objects under study (in particular, a slice of a geological sample) by using piecewise uniform regularization.
Keywords: tomography, phase correction, intensity transfer, regularization, ill-posed problem. .
Funding agency Grant number
Russian Foundation for Basic Research 19-51-53005-ГФЕН-а
Ministry of Education and Science of the Russian Federation 02.a03.21.0005
The authors were supported by the Russian Foundation for Basic Research (project no. 19-51-53005-GFEN-a) and the Competitiveness Increase Program of National Research Nuclear University “MEPhI” (project no. 02.a03.21.0005).
Received: 01.06.2020
Revised: 10.08.2020
Accepted: 10.09.2020
English version:
Journal of Applied and Industrial Mathematics, 2020, Volume 14, Issue 4, Pages 802–810
DOI: https://doi.org/10.1134/S1990478920040171
Bibliographic databases:
Document Type: Article
UDC: 519.632.4:519.642
Language: Russian
Citation: Ya. Wang, A. S. Leonov, D. V. Lukyanenko, V. D. Shinkarev, A. G. Yagola, “On phase correction in tomographic research”, Sib. Zh. Ind. Mat., 23:4 (2020), 18–29; J. Appl. Industr. Math., 14:4 (2020), 802–810
Citation in format AMSBIB
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\by Ya.~Wang, A.~S.~Leonov, D.~V.~Lukyanenko, V.~D.~Shinkarev, A.~G.~Yagola
\paper On phase correction in tomographic research
\jour Sib. Zh. Ind. Mat.
\yr 2020
\vol 23
\issue 4
\pages 18--29
\mathnet{http://mi.mathnet.ru/sjim1106}
\crossref{https://doi.org/10.33048/SIBJIM.2020.23.402}
\elib{https://elibrary.ru/item.asp?id=44970301}
\transl
\jour J. Appl. Industr. Math.
\yr 2020
\vol 14
\issue 4
\pages 802--810
\crossref{https://doi.org/10.1134/S1990478920040171}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85100166380}
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  • https://www.mathnet.ru/eng/sjim/v23/i4/p18
    • This publication is cited in the following 3 articles:
    1. Yu. P. Topolyuk, “Convergence of the Method of Regularization for Finding Normal Quasisolutions in Problems with Free Phase and a Completely Continuous Operator”, J Math Sci, 273:6 (2023), 960  crossref
    2. Stepanova I.E., Gudkova T.V., Salnikov A.M., Batov A.V., “A New Approach to Analytical Modeling of Mars'S Magnetic Field”, Inverse Probl. Sci. Eng., 30:1 (2022), 41–60  crossref  mathscinet  isi  scopus
    3. Yu. P. Topolyuk, “Convergence of the regularization method for finding a normal quasi-solution in problems with free phase with a completely continuous operator”, Mat. Met. Fiz. Mekh. Polya, 63:4 (2020)  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский журнал индустриальной математики
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