Pershina Y. Mathematical modelling in a computer tomography with use interflatation functions.

The method of restoration of spatially variable koefficient of absorption inside three-dimensional object under its known tomograms which lay in system of three groups of the crossed planes with the help of the operator polinomial interflatation functions of three variables is investigated in the dissertation. Also the method of restoration of koefficient of absorption inside a three-dimensional body under its tomograms in system of mutually perpendicular planes with use of the operator a spline - interflatation is investigated. This method gives higher accuracy, than classical restoration methods. For the first time the concept of the tomogram of mathematical sense as the trace from function of three variables on the set plane and is constructed algorithm of translation of the image of the tomogram in functional dependence which arguments is number of figure and coordinates of pixels is given. It enables to work with tomograms as with functions. Algorithmic and program realizations of methods are offered.