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Sibirskii Zhurnal Industrial'noi Matematiki, 2014, Volume 17, Number 3, Pages 98–110 (Mi sjim850)  
Recovering jumps in X-ray tomography

V. G. Romanov

Sobolev Institute of Mathematics SB RAS, 4 Koptyug av., 630090 Novosibirsk
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Abstract: The problem of finding the boundaries of the discontinuities and the jumps of a piecewise smooth function is considered for X-ray fan tomography. An algorithm of the reconstruction of unknown values and explicit formulas for their calculation are given. The original problem of X-ray tomography is reduced to a problem for a continuous piecewise differentiable function.
Keywords: tomography, determination of discontinuity lines, stability, uniqueness.
Received: 26.06.2014
English version:
Journal of Applied and Industrial Mathematics, 2014, Volume 8, Issue 4, Pages 582–593
DOI: https://doi.org/10.1134/S1990478914040164
Bibliographic databases:
Document Type: Article
UDC: 517.968
Language: Russian
Citation: V. G. Romanov, “Recovering jumps in X-ray tomography”, Sib. Zh. Ind. Mat., 17:3 (2014), 98–110; J. Appl. Industr. Math., 8:4 (2014), 582–593
Citation in format AMSBIB
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\by V.~G.~Romanov
\paper Recovering jumps in X-ray tomography
\jour Sib. Zh. Ind. Mat.
\yr 2014
\vol 17
\issue 3
\pages 98--110
\mathnet{http://mi.mathnet.ru/sjim850}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3364410}
\transl
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 4
\pages 582--593
\crossref{https://doi.org/10.1134/S1990478914040164}
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