Estimation of Discontinuous Functions of Two Variables with Unknown Discontinuity Lines (Rectangular Elements)

Lytvyn, Oleg M.; Pershina, Y. I.; Сергиенко, И. В.

doi:10.1007/s10559-014-9647-z

Cited by 6 publications

(2 citation statements)

References 5 publications

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“…Works [3]- [5] constructed the new information operators to solve the problems of computed tomography, where the paper [5] considers the heterogeneity of an internal structure of the body.…”

Section: Introductionmentioning

confidence: 99%

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

Mezhuyev¹,

Lytvyn²,

Lytvyn³

et al. 2019

IJMLC

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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.

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Section: Introductionmentioning

confidence: 99%

“…It should be noted that within the framework of classical computed tomography only the projections (integrals) are used. In the works [4], [5] the stated problem is formulated, but an explicit analytic solution is given only for the case when the systems of lines are mutually perpendicular.…”

Section: Introductionmentioning

confidence: 99%