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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2006, Volume 46, Number 1, Pages 18–25 (Mi zvmmf530)  
This article is cited in 2 scientific papers (total in 2 papers)

The statement and numerical solution of an optimization problem in X-ray tomography

D. S. Anikonova, I. V. Prokhorovb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences Sobolev Institute of Mathematics, Siberian Division, Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090, Russia
b Institute of Applied Mathematics, Far East Division, Russian Academy of Sciences, ul. Radio 7, Vladivostok, 690041, Russia
Full-text PDF (1337 kB) Citations (2)
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Abstract: A nonclassical problem is considered for the transport equation with coefficients depending on the energy of radiation. The task is to find the discontinuity surfaces for the coefficients of the equation from measurements of the radiation flux leaving the medium. For this tomography problem, an optimization problem is stated and numerically analyzed. The latter consists in determining the radiation energy that ensures the best reconstruction of the unknown medium. A simplified optimization problem is solved analytically.
Key words: radiation transfer equation, tomography, optimization problems.
Received: 24.09.2004
Revised: 07.07.2005
English version:
Computational Mathematics and Mathematical Physics, 2006, Volume 46, Issue 1, Pages 16–22
DOI: https://doi.org/10.1134/S0965542506010040
Bibliographic databases:
Document Type: Article
UDC: 519.626.2
Language: Russian
Citation: D. S. Anikonov, I. V. Prokhorov, “The statement and numerical solution of an optimization problem in X-ray tomography”, Zh. Vychisl. Mat. Mat. Fiz., 46:1 (2006), 18–25; Comput. Math. Math. Phys., 46:1 (2006), 16–22
Citation in format AMSBIB
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\by D.~S.~Anikonov, I.~V.~Prokhorov
\paper The statement and numerical solution of an optimization problem in X-ray tomography
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 1
\pages 18--25
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2239723}
\zmath{https://zbmath.org/?q=an:1170.78384}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 1
\pages 16--22
\crossref{https://doi.org/10.1134/S0965542506010040}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746075144}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    References:72
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