The method of restoring the internal structure of the 3D body based on the use of systems of three X-ray images and tomograms

Abstract

This article is devoted to the further generalization of low-angle tomography methods used by new information operators. It proposes and investigates a method of restoring the absorption coefficient of a 3D body using penetrating irradiation in three mutually perpendicular directions and three systems of tomograms in planes perpendicular to these directions. For modeling, the spline interflatation of functions of three variables, in which the basis functions are splines of the first power, is studied in more detail.Without losing generality, it is assumed that the investigated object is located in a unit cube, the edges of which are parallel to the corresponding coordinate axes. Theorems about the approximate properties of constructed operators that approximate the absorption coefficient are formulated and proved. In particular, the theorem on the remainder of the approximation is proved.