Operators of the interflatation of functions of 3 variables in the 3D computer tomography

Abstract

Interlineation of the functions of many variables is the restoration of these functions with the help of their traces and the traces of their partial derivatives (or some other differential operators) up to a given order on a system of lines. Interflation (interflatation) of the functions of many variables is the restoration of these functions with the help of their traces and the traces of their partial derivatives (or some other differential operators) up to a given order on a system of surfaces (in particular, on flat surfaces). Interlineation and interflatation are the natural generalizations of interpolation of functions of many variables. Here, solutions to the 3D problems of computer tomography using operators of interflatation of functions of 3 variables are proposed. In particular, a review of recent results in this direction will be given. Concrete algorithms for operators of interflatation with given projections on flat systems will be formulated. Thus, the authors offer a new method of constructing a mathematical model of an X-ray computer tomography, which does not demand use of the spiral scheme of scanning and is based on any of the known classical schemes of reception of tomograms.