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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2020, Volume 13, Issue 1, Pages 95–106 (Mi vyuru533)  

Programming and Computer Software

Fast X-ray sum calculation algorithm for computed tomography problem

K. B. Bulatovab, M. V. Chukalinacd, D. P. Nikolaevd

a Federal Research Center Computer Science and Control of the Russian Academy of Sciences, Moscow, Russian Federation
b Smart Engines Service LLC, Moscow, Russian Federation
c FSRC Crystallography and Photonics of the Russian Academy of Sciences, Moscow, Russian Federation
d Institute for Information Transmission Problems of the Russian Academy of Sciences, Moscow, Russian Federation

Abstract: In iterative methods of computed tomography, each iteration requires to calculate a multitude of sums over values for the current reconstruction approximation. Each summable set is an approximation of a straight line in the three-dimensional space. In a cone-beam tomography, the number of sums to be calculated on each iteration has a cubic dependence on the linear size of the reconstructed image. Direct calculation of these sums requires the number of summations in a quartic dependence on the linear image size, which limits the performance of the iterative methods. The novel algorithm proposed in this paper approximates the three-dimensional straight lines using dyadic patterns, and, using the adjustment of precalculation and inference complexity similar to the adjustment employed in the Method of Four Russians, provides the calculation of these sums with a sub-quartic dependence on the linear size of the reconstructed image.

Keywords: computed tomography, algebraic reconstruction, fast Radon transform, fast Hough transform, Method of Four Russians.

DOI: https://doi.org/10.14529/mmp200107

Full text: PDF file (279 kB)
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UDC: 519.612+616-073.756.8
MSC: 65R10, 97N70
Received: 07.10.2019
Language:

Citation: K. B. Bulatov, M. V. Chukalina, D. P. Nikolaev, “Fast X-ray sum calculation algorithm for computed tomography problem”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 13:1 (2020), 95–106

Citation in format AMSBIB
\Bibitem{BulChuNik20}
\by K.~B.~Bulatov, M.~V.~Chukalina, D.~P.~Nikolaev
\paper Fast X-ray sum calculation algorithm for computed tomography problem
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2020
\vol 13
\issue 1
\pages 95--106
\mathnet{http://mi.mathnet.ru/vyuru533}
\crossref{https://doi.org/10.14529/mmp200107}
\elib{https://elibrary.ru/item.asp?id=42661920}


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