A fast algorithm for the inversion of Abel's transform

DOI10.1016/j.amc.2016.12.009zbMath1411.65159OpenAlexW2567179384MaRDI QIDQ1735233

Enrico De Micheli

Publication date: 28 March 2019

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

Full work available at URL: https://doi.org/10.1016/j.amc.2016.12.009

zbMATH Keywords

inverse problemsLegendre polynomialsAbel inversionstability estimatesplasma emission coefficientsradio occultation

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Numerical methods for integral transforms (65R10) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10)

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Cites Work

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• An approximate method for Abel inversion using Chebyshev polynomials
• Quantitative Abel tomography robust to noisy, corrupted and missing data
• Quadrature rule for Abel's equations: Uniformly approximating fractional derivatives
• Abel integral equations. Analysis and applications
• Fredholm integral equations of the first kind and topological information theory
• Operator theoretic treatment of linear Abel integral equations of first kind
• A Jacobi–Legendre polynomial-based method for the stable solution of a deconvolution problem of the Abel integral equation type
• Stable inversion of the Abel integral equation of the first kind by means of orthogonal polynomials
• Abel inversion using total variation regularization: applications
• Quantitative Object Reconstruction Using Abel Transform X-Ray Tomography and Mixed Variable Optimization
• A Fast Algorithm for the Evaluation of Legendre Expansions
• A Stochastic Roundoff Error Analysis for the Fast Fourier Transform
• A new Abel inversion by means of the integrals of an input function with noise
• On weakly bounded noise in ill-posed problems
• Accelerating the Nonuniform Fast Fourier Transform
• Inversion of Abel’s Integral Equation by Means of Orthogonal Polynomials
• A new method of solving noisy Abel-type equations

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