Application of optimal quadrature formulas for reconstruction of CT images

DOI10.1016/j.cam.2020.113313zbMath1460.65025OpenAlexW3112158372WikidataQ113878739 ScholiaQ113878739MaRDI QIDQ2223883

Soomin Jeon, Kholmat Mahkambaevich Shadimetov, Abdullo Rakhmonovich Hayotov

Publication date: 3 February 2021

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2020.113313

zbMATH Keywords

Fourier transformSobolev spaceRadon transformoptimal quadrature formulaerror functionalCT image reconstructionfiltered back-projection method

Mathematics Subject Classification ID

Interpolation in approximation theory (41A05) Spline approximation (41A15) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Numerical methods for trigonometric approximation and interpolation (65T40)

Related Items (5)

Оптимальные квадратурные формулы в пространстве W2(m,m−1) периодических функций ⋮ Optimal formulas for the approximate-analytical solution of the general Abel integral equation in the Sobolev space ⋮ Optimal quadrature formulas for oscillatory integrals in the Sobolev space ⋮ Implicit upwind difference scheme for a symmetric \(t\)-hyperbolic system with variable coefficients and lowest terms ⋮ Optimal quadrature formulas for calculating integrals of rapidly oscillating functions

Cites Work

• Complexity of oscillatory integration for univariate Sobolev spaces
• Construction of optimal quadrature formulas for Fourier coefficients in Sobolev space \(L_{2}^{(m)}(0,1)\)
• Numerical calculation of integrals involving oscillatory and singular kernels and some applications of quadratures
• Efficient computation of highly oscillatory integrals with Hankel kernel
• Optimal quadrature formulas for the Sobolev space \(H^1\)
• On an optimal quadrature formula for approximation of Fourier integrals in the space \(L_2^{( 1 )}\)
• Numerical approximation of vector-valued highly oscillatory integrals
• Numerical Integration of Highly Oscillating Functions
• Computing Highly Oscillatory Integrals
• OPTIMAL QUADRATURE FORMULAS FOR FOURIER COEFFICIENTS IN <i>W</i>₂^{(<i>m</i>,<i>m</i>-1)} 2 SPACE
• Efficient quadrature of highly oscillatory integrals using derivatives
• The Mathematics of Medical Imaging
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