Loading [MathJax]/jax/output/SVG/config.js
Sibirskii Zhurnal Industrial'noi Matematiki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Sib. Zh. Ind. Mat.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Sibirskii Zhurnal Industrial'noi Matematiki, 2014, Volume 17, Number 4, Pages 48–59 (Mi sjim858)  
This article is cited in 3 scientific papers (total in 3 papers)

Approximate recovery of a function given in a domain with low refraction from the ray integrals of the function

E. Yu. Derevtsovab, S. V. Maltsevaab, I. E. Svetovba

a Sobolev Institute of Mathematics SB RAS, 4 Koptyug av., 630090 Novosibirsk
b Novosibirsk State University, 2 Pirogova st., 630090 Novosibirsk
Full-text PDF (613 kB) Citations (3)
References:
PDF
HTML
Abstract: We suggest an approach to the recovery of a function given in a Riemannian domain with low refraction from the ray integrals of the function. We construct an inversion algorithm with the use of the back-projection operator and the fast Fourier transform. The algorithm is investigated by numerical methods.
Keywords: tomography, refraction, ray transform, back-projection operator, inversion formula, fast Fourier transform.
Received: 25.06.2014
English version:
Journal of Applied and Industrial Mathematics, 2015, Volume 9, Issue 1, Pages 36–46
DOI: https://doi.org/10.1134/S1990478915010056
Bibliographic databases:
Document Type: Article
UDC: 517.98+519.677
Language: Russian
Citation: E. Yu. Derevtsov, S. V. Maltseva, I. E. Svetov, “Approximate recovery of a function given in a domain with low refraction from the ray integrals of the function”, Sib. Zh. Ind. Mat., 17:4 (2014), 48–59; J. Appl. Industr. Math., 9:1 (2015), 36–46
Citation in format AMSBIB
\Bibitem{DerMalSve14}
\by E.~Yu.~Derevtsov, S.~V.~Maltseva, I.~E.~Svetov
\paper Approximate recovery of a~function given in a~domain with low refraction from the ray integrals of the function
\jour Sib. Zh. Ind. Mat.
\yr 2014
\vol 17
\issue 4
\pages 48--59
\mathnet{http://mi.mathnet.ru/sjim858}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3364392}
\transl
\jour J. Appl. Industr. Math.
\yr 2015
\vol 9
\issue 1
\pages 36--46
\crossref{https://doi.org/10.1134/S1990478915010056}
Linking options:
  • https://www.mathnet.ru/eng/sjim858
  • https://www.mathnet.ru/eng/sjim/v17/i4/p48
    • This publication is cited in the following 3 articles:
    1. E Yu Derevtsov, “On constructing the Riemannian metrics in refraction tomography problems”, J. Phys.: Conf. Ser., 1715:1 (2021), 012033  crossref
    2. Maltseva V S. Svetov I.E. Polyakova A.P., “Reconstruction of a Function and Its Singular Support in a Cylinder By Tomographic Data”, Eurasian J. Math. Comput. Appl., 8:2 (2020), 86–97  crossref  isi  scopus
    3. E. Yu. Derevtsov, S. V. Maltseva, I. E. Svetov, “Priblizhennoe obraschenie operatora luchevogo preobrazovaniya v refraktsionnoi tomografii”, Sib. elektron. matem. izv., 11 (2014), 833–856  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский журнал индустриальной математики
    Statistics & downloads:
    Abstract page:282
    Full-text PDF :102
    References:51
    First page:6
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025