Investigation of scattering and absorbing media by the methods of X-ray tomography

Investigation of scattering and absorbing media by the methods of X-ray tomography -- The aim of X-ray tomography is to determine the internal structure of a medium by analyzing how the radioactive particles pass through the medium. This problem is considered here as an inverse problem for the equation of radiation transport. We prove two uniqueness theorems for determining the attenuation coefficient provided that only the radiation intensity at the boundary of the medium is known. Formulae for the Radon transforms of the sought-for function are obtained and used to construct the algorithms for finding the attenuation coefficient. Computational examples for a test problem are presented. The results can be used in tomography for a medium with internal sources and quite arbitrary scattering of particles. The ideas of the previous work by D. S. Anikonov [1] are developed in this paper. We consider an inverse problem for the transport equation which is to determine the main characteristic of a medium, namely, the radiation attenuation coefficient. Its specific feature is that the information provided for the attenuation coefficient is independent of the other characteristics of the medium. This is of major importance in tomography. The basic concepts of the transport theory and exact formulations of inverse and direct problems are given http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Inverse and Ill-Posed Problems de Gruyter

Investigation of scattering and absorbing media by the methods of X-ray tomography

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Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0928-0219
eISSN
1569-3945
DOI
10.1515/jiip.1993.1.4.259
Publisher site
See Article on Publisher Site

Abstract

-- The aim of X-ray tomography is to determine the internal structure of a medium by analyzing how the radioactive particles pass through the medium. This problem is considered here as an inverse problem for the equation of radiation transport. We prove two uniqueness theorems for determining the attenuation coefficient provided that only the radiation intensity at the boundary of the medium is known. Formulae for the Radon transforms of the sought-for function are obtained and used to construct the algorithms for finding the attenuation coefficient. Computational examples for a test problem are presented. The results can be used in tomography for a medium with internal sources and quite arbitrary scattering of particles. The ideas of the previous work by D. S. Anikonov [1] are developed in this paper. We consider an inverse problem for the transport equation which is to determine the main characteristic of a medium, namely, the radiation attenuation coefficient. Its specific feature is that the information provided for the attenuation coefficient is independent of the other characteristics of the medium. This is of major importance in tomography. The basic concepts of the transport theory and exact formulations of inverse and direct problems are given

Journal

Journal of Inverse and Ill-Posed Problemsde Gruyter

Published: Jan 1, 1993

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