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Sibirskii Zhurnal Industrial'noi Matematiki, 2014, Volume 17, Number 1, Pages 8–17 (Mi sjim814)  
Numerical realization of the algorithm of reconstruction of an inhomogeneous medium for an X-ray tomography problem

E. Yu. Balakinaab

a Sobolev Institute of Mathematics, 4 Koptyug av., 630090 Novosibirsk
b Novosibirsk State University, 2 Pirogova st., 630090 Novosibirsk
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Abstract: We study an X-ray tomography problem which is an inverse problem for the differential transport equation. We take into account the absorption of particles by the medium and their single scattering. The statement of the problem corresponds to multiple probing. The medium is unknown; the densities of the output flux averaged over energy are given. The object in question is the discontinuity surfaces of the coefficients of the equation. This corresponds to searching for the boundaries between various substances contained in the medium that we probe. The solution is constructive, and a version of numerical realization of the algorithm is presented.
Keywords: free boundary, transport equation, inverse problem, multiple probing, tomography.
Received: 12.11.2013
English version:
Journal of Applied and Industrial Mathematics, 2014, Volume 8, Issue 2, Pages 158–167
DOI: https://doi.org/10.1134/S1990478914020021
Bibliographic databases:
Document Type: Article
UDC: 519.688
Language: Russian
Citation: E. Yu. Balakina, “Numerical realization of the algorithm of reconstruction of an inhomogeneous medium for an X-ray tomography problem”, Sib. Zh. Ind. Mat., 17:1 (2014), 8–17; J. Appl. Industr. Math., 8:2 (2014), 158–167
Citation in format AMSBIB
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\by E.~Yu.~Balakina
\paper Numerical realization of the algorithm of reconstruction of an inhomogeneous medium for an X-ray tomography problem
\jour Sib. Zh. Ind. Mat.
\yr 2014
\vol 17
\issue 1
\pages 8--17
\mathnet{http://mi.mathnet.ru/sjim814}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3379249}
\transl
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 2
\pages 158--167
\crossref{https://doi.org/10.1134/S1990478914020021}
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