Abstract:
In this article we consider problems of reconstruction of a function and its singular support by using tomographic data. The data for the problems are values of the attenuated geodesic x-ray transform which is a set of integrals of an unknown function calculated along geodesics of the Riemannian metric that is used for modelling refraction in a cylinder. The values of the attenuated geodesic x-ray transform are received in a slice-by-slice fan-beam scheme. Our approach is based on the slice-by-slice reconstruction of the sought-for function or its singular support using a modification of well-known operators of back-projection and break indicator.
Citation:
S. V. Mal'tseva, I. E. Svetov, A. P. Polyakova, “Reconstruction of a function and its singular support in a cylinder by tomographic data”, Eurasian Journal of Mathematical and Computer Applications, 8:2 (2020), 86–97
\Bibitem{MalSvePol20}
\by S.~V.~Mal'tseva, I.~E.~Svetov, A.~P.~Polyakova
\paper Reconstruction of a function and its singular support in a cylinder by tomographic data
\jour Eurasian Journal of Mathematical and Computer Applications
\yr 2020
\vol 8
\issue 2
\pages 86--97
\mathnet{http://mi.mathnet.ru/ejmca160}
\crossref{https://doi.org/10.32523/2306-6172-2020-8-2-86-97}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85087004392}
Linking options:
https://www.mathnet.ru/eng/ejmca160
https://www.mathnet.ru/eng/ejmca/v8/i2/p86
This publication is cited in the following 1 articles:
E. O. Kovalenko, I. V. Prokhorov, “Localization of the Discontinuity Lines of the Bottom Scattering Coefficient According to Acoustic Sounding Data”, J. Appl. Ind. Math., 16:1 (2022), 70
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