Litvin O. The Mathematical modeling in littleforeshortening computer tomography by means of interlineation and blending approximation functions.

In dissertation work built and probed mathematical models of flat task by x-ray computer tomography with the use of the set projections on the system lines. The mathematical model looks like the interlineation operators (operators who restore functions of two and more variables with the help of their traces on the specified system of lines) in which known projections on the set system of straight lines are explicit used. The operator has such property: integrals from him along corresponding straight lines are equal to the set projections irrespective of a choice of some systems of parameters. The choice of the specified parameters is carried out by minimization special fuctional. At construction of the interlineation operators with known projections on given system of straight lines use the operators of interpolation of functions of one variable offered and investigated in work on fixed system of points. Methods of designing of three-dimensional mathematical models of internal structure of a body (alsoare offered to density, factor of absorption or easing) in the ultralittleforeshortening a computer tomography by blending approximation operators of the functions of three variables by operators which allow to build three-dimensional mathematical model of a body with the help finite Fouirer sums of the approximate functions on two or three variables. These mathematical models of internal structure of a three-dimensional body use only two or three x-ray pictures in mutual - perpendicular directions. It is investigated classes of objects, which can precisely possible to restore with the help of two or three x-ray pictures the offered method.