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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 2, Pages 318–335
DOI: https://doi.org/10.7868/S0044466914020033
(Mi zvmmf9994)
 

Layerwise sensing in $X$-ray tomography in the polychromatic case

E. Yu. Balakinaab

a Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, ul. Koptyuga 4, Novosibirsk, 630090, Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia
References:
Abstract: An $X$-ray tomography problem that is an inverse problem for the transport differential equation is studied. The absorption and single scattering of particles are taken into account. The suggested statement of the problem corresponds to stepwise and layerwise sensing of an unknown medium with initial data specified as the integrals of the outgoing flux density with respect to energy. The sought object is a set on which the coefficients of the equations suffer a discontinuity, which corresponds to searching for the boundaries between the different substances composing the sensed medium. A uniqueness theorem is proven under rather general assumptions and a condition guaranteeing the existence of the sought lines. The proof is constructive and can be used for developing a numerical algorithm.
Key words: unknown boundary, transport equation, inverse problems, tomography, layerwise sensing, uniqueness theorem.
Received: 10.09.2013
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 2, Pages 335–352
DOI: https://doi.org/10.1134/S0965542514020031
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: E. Yu. Balakina, “Layerwise sensing in $X$-ray tomography in the polychromatic case”, Zh. Vychisl. Mat. Mat. Fiz., 54:2 (2014), 318–335; Comput. Math. Math. Phys., 54:2 (2014), 335–352
Citation in format AMSBIB
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