-- 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  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 of Inverse and Ill-Posed Problems – de Gruyter
Published: Jan 1, 1993
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