UDC 519.6
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2 Kharkiv National University of Radio Electronics, Kharkiv, Ukraine
 litvinog@ukr.net
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ANALYSIS OF THE RESULTS OF A COMPUTING<>EXPERIMENT TO RESTORE
THE DISCONTINUOUS FUNCTIONS OF TWO VARIABLES USING PROJECTIONS. II
Abstract. This article continues a series of publication under the same name. It performs further improvement of the method for recovering discontinuous functions of two variables using projections in order to improve the accuracy of approximation without the Gibbs phenomenon. To this end, it is proposed to construct a discontinuous spline so that the difference between the function being approximated and this spline is a differentiable function. This function is restored using finite Fourier sums whose Fourier coefficients are found using projections. A method for calculating these coefficients is proposed. In the computing experiment, it was assumed that the approximated function has discontinuities of the first kind on a given system of circles or ellipses nested into each other. Analysis of the calculation results confirmed the theoretical statement of the study. The method makes it possible to obtain a prescribed approximation accuracy with a smaller number of projections, i.e., with less irradiation.
Keywords: computed tomography, discontinuous function, discontinuous spline, differentiability class, Gibbs phenomenon, Fourier sum.
FULL TEXT
REFERENCES
- Lytvyn O.M., Lytvyn O.G. Analysis of the results of a computational experiment to restore the discontinuous functions of two variables using projections. I. Kibernetyka ta systemnyj analiz. 2021. Vol. 57, N 5. P. 98–107.
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- Lytvyn O.M., Lytvyn O.G. On an approach to the approximation of discontinuous functions using projections and finite Fourier sums. Computational methods and systems of information transformation: Proc. V sci.-tehn. conf. (Lviv, October 4-5, 2018). Lviv: FMI NASU, 2018. P. 8–11.
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