Scattered-Radiation Problem in Three-Dimensional Transmission Tomography

A.V.Likhachov and V.V.Pickalov

Institute of Theoretical and Applied Mechanics SB RAS, 4/1, Institutskaya Street, Novosibirsk 630090, Russia, likhache@itam.nsc.ru

ABSTRACT

Implementations of three-dimensional tomography to non-destructive testing of objects in engineering and industry are considered. Problems caused by the contribution of scattered photons to measured signal are addressed. It is assumed that a photoelectric interaction between the radiation and the medium occurs under conditions of the ray tomography approximation. Both single- and multiple- scattering processes are discussed. Two special methods for eliminating the detrimental effects caused by scattering are developed. One of these methods is based on the Neumann-series decomposition of the product of the radiation-propagation operator for the case with scattering and the operator that solves the pure transmission tomography problem. The other method makes use of the fact that each set of exact projections must be a self-consistent one since these projections all belong to one and the same object. The latter provides the possibility to reconstruct them with good accuracy. By numerical simulations, both methods were proved to be quite effective.

Key words 3D-tomography, scattering, Neumann series, self-consistent of data