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Sibirskii Zhurnal Industrial'noi Matematiki, 2013, Volume 16, Number 2, Pages 62–71 (Mi sjim780)  
Estimation of the efficiency of the method of hierarchical reconstruction for the problem of the reconstruction of discrete scattering centers from projections

A. N. Bondarenkoa, V. A. Dedoka, L. A. Kozinkinb, M. P. Tokarevc

a Sobolev Institute of Mathematics of SB RAS, 4 Koptyug av., 630090 Novosibirsk, Russia
b Novosibirsk State University, 2 Pirogova st., 630090 Novosibirsk, Russia
c Kutateladze Institute of Thermophysics of SB RAS, 1 Lavrent'ev av., 630090 Novosibirsk, Russia
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Abstract: We study the actual problem of determining the maximal set for the set of points in $\mathbb R^3$ from the set of two-dimensional projections. This problem arises naturally in the applications of physical hydrodynamics for the optical diagnostics of real flows of liquid and gas by measuring the instantaneous rate fields in the volume of flow. We propose a method for reconstructing the given set and determining the sufficiency of the measurements for the uniqueness of a solution to the inverse problem for parallel and perspective projections. A statistical evaluation for the efficiency of the reconstruction method is obtained.
Keywords: 3D reconstruction of point objects, particle image velocimetry, 3D PTV, inverse problems.
Received: 20.02.2013
English version:
Journal of Applied and Industrial Mathematics, 2013, Volume 7, Issue 3, Pages 335–343
DOI: https://doi.org/10.1134/S199047891303006X
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: A. N. Bondarenko, V. A. Dedok, L. A. Kozinkin, M. P. Tokarev, “Estimation of the efficiency of the method of hierarchical reconstruction for the problem of the reconstruction of discrete scattering centers from projections”, Sib. Zh. Ind. Mat., 16:2 (2013), 62–71; J. Appl. Industr. Math., 7:3 (2013), 335–343
Citation in format AMSBIB
\Bibitem{BonDedKoz13}
\by A.~N.~Bondarenko, V.~A.~Dedok, L.~A.~Kozinkin, M.~P.~Tokarev
\paper Estimation of the efficiency of the method of hierarchical reconstruction for the problem of the reconstruction of discrete scattering centers from projections
\jour Sib. Zh. Ind. Mat.
\yr 2013
\vol 16
\issue 2
\pages 62--71
\mathnet{http://mi.mathnet.ru/sjim780}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3203342}
\transl
\jour J. Appl. Industr. Math.
\yr 2013
\vol 7
\issue 3
\pages 335--343
\crossref{https://doi.org/10.1134/S199047891303006X}
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    		Сибирский журнал индустриальной математики
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