External sources of resonance type in X-ray tomography : Journal of Inverse and Ill-posed Problems

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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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External sources of resonance type in X-ray tomography

D. S. Anikonov1

1Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Acad. Koptyug prosp., 4, 630090 Novosibirsk, Russia. Email:

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 17, Issue 4, Pages 311–320, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2009.021, June 2009

Publication History

Received:
2008-03-21
Published Online:
2009-06-16

Abstract

In this paper the author consider uniqueness of solution of determining attenuation coefficient of X-ray radiation inside absorbing and scattering medium. The known data are densities of incoming and outgoing flows of radiation in the boundary of the medium. The specific character of the problem is that the density of external sources of radiation depending on energy is disconnected in the finite number of points which corresponds to the radiation resonance. This assumption is sufficient to successful research of the problem which may be considered as the problem of X-ray tomography. The generality of the mathematical model used in research makes possible to apply the result for other problems of radiation tomography.

Key words.: Resonance; tomography; radiation; inverse problems; transport equation

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