IJMLC 2019 Vol.9(2): 154-159 ISSN: 2010-3700
DOI: 10.18178/ijmlc.2019.9.2.780

Operators of Approximation of Functions f(x, y) by their Projections on the System of Nonparallel Lines for Computed Tomography

Vitaliy Mezhuyev, Oleh M. Lytvyn, Oleh O. Lytvyn, Iuliia I. Pershyna, Olesia P. Nechuiviter, and Yevheniia L. Khurdei

Abstract—Operators of approximation of the functions of two variables, interpolating the functions by their projections along M nonparallel lines, were not sufficiently considered in the scientific literature. At the same time, this theoretical problem has a strong practical interest when the given projections (integrals along lines) come from a computed tomography scanner. The paper constructs the interpolation operator which exactly restores the polynomials of degree M-1. The method was investigated for a system of mutually perpendicular lines and for three nonparallel intersecting lines (sides of a triangle). An integral representation of the residual member of the approximation by the obtained operators for differentiable functions is found. The proposed method allows to expand theory and practical applications of computed tomography.

Index Terms—Computed tomography, approximation, operators of interpolation, projections among lines.

Vitaliy Mezhuyev is with the University Malaysia Pahang, Gambang, Malaysia (e-mail: vitaliy@ump.edu.my).
Oleh M. Lytvyn, Oleh O. Lytvyn, Iuliia I. Pershyna, Olesia P. Nechuiviter and Yevheniia L. Khurdei are with the Ukrainian Engineering and Pedagogical Academy, Kharkiv, Ukraine (e-mails: academ_mail@ukr.net, loo71@bk.ru, yulia_pershina@mail.ru, olesya@email.com, evgesha.hurdei@gmail.com).

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Cite: Vitaliy Mezhuyev, Oleh M. Lytvyn, Oleh O. Lytvyn, Iuliia I. Pershyna, Olesia P. Nechuiviter, and Yevheniia L. Khurdei, "Operators of Approximation of Functions f(x, y) by their Projections on the System of Nonparallel Lines for Computed Tomography," International Journal of Machine Learning and Computing vol. 9, no. 2, pp. 154-159, 2019.

General Information

  • ISSN: 2010-3700 (Online)
  • Abbreviated Title: Int. J. Mach. Learn. Comput.
  • Frequency: Bimonthly
  • DOI: 10.18178/IJMLC
  • Editor-in-Chief: Dr. Lin Huang
  • Executive Editor:  Ms. Cherry L. Chen
  • Abstracing/Indexing: Scopus (since 2017), EI (INSPEC, IET), Google Scholar, Crossref, ProQuest, Electronic Journals Library.
  • E-mail: ijmlc@ejournal.net