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Sibirskii Zhurnal Industrial'noi Matematiki, 2011, Volume 14, Number 2, Pages 21–27 (Mi sjim662)  
This article is cited in 9 scientific papers (total in 9 papers)

The problem of single-beam probing of an unknown medium

D. S. Anikonova, V. G. Nazarovb, I. V. Prokhorovb

a Sobolev Institute of Mathematics SB RAS, Novosibirsk, RUSSIA
b Institute of Applied Mathematics FEB RAS, Vladivostok, RUSSIA
Full-text PDF (283 kB) Citations (9)
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Abstract: We propose an algorithm for determining the shadows of unknown bodies inside an arbitrary medium probed by radiation only in one direction. We demonstrate a successful performance of the algorithm in the case that on a direct visualization (a photograph) the bodies under consideration are indistinguishable. We study the problem of overlapping the shadows of some objects by others and conclude that this circumstance can improve or worsen the quality of reconstruction depending on the radiation characteristics of the medium. The presented results of numerical experiments show good agreement between theoretical and computational methods.
Keywords: radiation transfer equation, X-ray tomography.
Received: 21.05.2010
English version:
Journal of Applied and Industrial Mathematics, 2011, Volume 5, Issue 4, Pages 500–505
DOI: https://doi.org/10.1134/S1990478911040041
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: D. S. Anikonov, V. G. Nazarov, I. V. Prokhorov, “The problem of single-beam probing of an unknown medium”, Sib. Zh. Ind. Mat., 14:2 (2011), 21–27; J. Appl. Industr. Math., 5:4 (2011), 500–505
Citation in format AMSBIB
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\by D.~S.~Anikonov, V.~G.~Nazarov, I.~V.~Prokhorov
\paper The problem of single-beam probing of an unknown medium
\jour Sib. Zh. Ind. Mat.
\yr 2011
\vol 14
\issue 2
\pages 21--27
\mathnet{http://mi.mathnet.ru/sjim662}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2962150}
\elib{https://elibrary.ru/item.asp?id=18016217}
\transl
\jour J. Appl. Industr. Math.
\yr 2011
\vol 5
\issue 4
\pages 500--505
\crossref{https://doi.org/10.1134/S1990478911040041}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-82655170467}
Linking options:
  • https://www.mathnet.ru/eng/sjim662
  • https://www.mathnet.ru/eng/sjim/v14/i2/p21
    • This publication is cited in the following 9 articles:
    1. E. O. Kovalenko, I. V. Prokhorov, “Lokalizatsiya linii razryva koeffitsienta donnogo rasseyaniya po dannym akusticheskogo zondirovaniya”, Sib. zhurn. industr. matem., 25:1 (2022), 67–79  mathnet  crossref
    2. E. O. Kovalenko, I. V. Prokhorov, “Localization of the Discontinuity Lines of the Bottom Scattering Coefficient According to Acoustic Sounding Data”, J. Appl. Ind. Math., 16:1 (2022), 70  crossref
    3. E. O. Kovalenko, I. V. Prokhorov, “Opredelenie koeffitsienta donnogo rasseyaniya pri mnogoluchevom zondirovanii okeana”, Dalnevost. matem. zhurn., 19:2 (2019), 206–222  mathnet
    4. V. G. Nazarov, “Uluchshenie kachestva izobrazhenii v kompyuternoi tomografii spomoschyu integralnogo preobrazovaniya spetsialnogo vida”, Kompyuternye issledovaniya i modelirovanie, 7:5 (2015), 1033–1046  mathnet  crossref
    5. Mikhail Guzev, Vasilii Nazarov, Igor Prokhorov, “Modelling of Material Composition in X-Ray Diagnostics”, AMM, 749 (2015), 116  crossref
    6. E. Yu. Balakina, “Numerical realization of the algorithm of reconstruction of an inhomogeneous medium for an X-ray tomography problem”, J. Appl. Industr. Math., 8:2 (2014), 158–167  mathnet  crossref  mathscinet
    7. D. S. Anikonov, V. G. Nazarov, I. V. Prokhorov, “The integro-differential indicator for a problem of single-beam tomography”, J. Appl. Industr. Math., 8:3 (2014), 301–306  mathnet  crossref  mathscinet
    8. A. S. Zhuplev, I. V. Prokhorov, I. P. Yarovenko, “Statisticheskoe modelirovanie transporta elektronov v zadachakh vizualizatsii neodnorodnykh sred”, Dalnevost. matem. zhurn., 14:2 (2014), 217–230  mathnet
    9. D. S. Anikonov, V. G. Nazarov, “Problem of two-beam tomography”, Comput. Math. Math. Phys., 52:3 (2012), 315–320  mathnet  crossref  zmath  adsnasa  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
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