Cybernetics And Systems Analysis
International Theoretical Science
Journal
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1 Ukrainian Engineering Pedagogics Academy, Kharkiv, Ukraine
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2 Kharkiv National University of Radio Electronics, Kharkiv, Ukraine
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Abstract. The authors provide the main statements of the method of approximation of discontinuous functions of two variables that describe an image of the surface of a 2D-body or an image of the internal structure of a 3D-body in a certain plane, using the projections from a computer tomograph. The method is based on specially designed discontinuous two-variable splines and finite Fourier sums whose Fourier coefficients can be found using the projection data. The difference between the function being approximated and the specified discontinuous spline is a continuous function and can be approximated by finite Fourier sums without the Gibbs phenomenon. In the computational experiment, it was assumed that the approximated function has discontinuities of the first kind on a given system of circles and ellipses nested into each other. Analysis of the calculation results confirmed the theoretical statements of the study. The proposed method makes it possible to obtain a prescribed approximation accuracy with a smaller number of projections, that is, with less irradiation.
Keywords: computer tomography, discontinuous function, discontinuous spline, Fourier sum.
