The Mathematical Modelling in the Computer Tomography with using Direct Fourier Method and Spline-Interlineation of the Functions

K.E. Babenko and O.N. Lytvyn (Ukraine)


Computer tomography, direct Fourier method, FFT, spline-interlineation of the functions.


The article is devoted to improvement of mathematical model a X-ray computer tomograph on the basis of direct method Fourier, kvadrature formulas with even number of knots, exact on polynomials and splines of the second order and a spline interlineation of functions of two variables. This kvadrature formula removes restrictions on parity or oddness of number of projections, acting on from a computer tomograph. It can be used (together with kvadrature Simpson's formula, demanding the odd number of knots) in serial tomographs. On a basis a spline interlineation of functions with property are development such updating of direct Fourier method which allows to reduce asymptotical twice quantity of arithmetic operations. ( ) ( xyfyxf ,, = ) The algorithm on basis FFT for effective calculation of full Fourier sums of two variables is developed. The algorithm is used at visualization in mathematical model X-ray tomographs.

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