Abel inversion method using Chebyshev wavelets for tomographic reconstruction of an axisymmetric medium

ELFAGRICH, Mahfoud; Said, Abdessadek Ait Haj; Fagrich, Kamal El

doi:10.1364/ao.424172

Cited by 4 publications

(1 citation statement)

References 23 publications

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“…Computing Abel inversion by using orthogonal polynomials is also a common method and has been endowed a great interest for a long time [28][29][30][31][32]. The main principle of this type of approach is to expand the input measured data and the desired solutions into orthogonal polynomials, coupled with the exact inversion of the Abel integral operator.…”

Section: Introductionmentioning

confidence: 99%

A new Abel inversion algorithm by using legendre polynomials

Pang¹,

Shi

Liu

et al. 2023

Phys. Scr.

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Abel’s integral equation is frequently used in many areas of physics to reconstruct the radial physical quantity distribution from its projection data. In this paper, a new effective and accurate Abel inversion algorithm based on shifted Legendre polynomials is proposed and analyzed. The proposed method is derivative-free and singularity-free. Both the input projection data and the unknown solutions of the Abel’s integral equation are approximately expressed as Legendre expansions. A Legendre operational matrix of integral is constructed and then reduced to a discrete algebraic sum, which makes it easy and fast to compute the coefficients matrix of approximate solutions for the inverse Abel transform. Finally, the accuracy and stability are proved and then illustrated by some numerical experiments widely used in plasma diagnostics.

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Section: Introductionmentioning

confidence: 99%

A new Abel inversion algorithm by using legendre polynomials

Pang¹,

Shi

Liu

et al. 2023

Phys. Scr.

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Interferometric Data Analysis of Convective Heat Transfer under a Downward-Facing Horizontal Circular Plate

Said¹,

ELFAGRICH²,

Dahani

2023

J Eng Phys Thermophy

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Evaluation of the Abel inversion integral in O-mode plasma reflectometry using Chebyshev–Gauss quadrature

Leppink

Lau

Lin

et al. 2023

Review of Scientific Instruments

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The Abel transform is often used to reconstruct plasma density profiles from O-Mode polarized reflectometry diagnostics. However, standard numerical trapezoidal evaluation of the Abel inversion integral can be computationally expensive for a large number of evaluation points, and an endpoint singularity exists on the upper-bound of the integral, which can result in an increased error. In this work, Chebyshev–Gauss quadrature is introduced as a new method to evaluate the Abel inversion integral for the problem of O-Mode plasma reflectometry. The method does not require numerical evaluation of an integral singularity and is shown to have similar accuracy compared to existing methods while being computationally efficient.

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Abel inversion method using Chebyshev wavelets for tomographic reconstruction of an axisymmetric medium

Cited by 4 publications

References 23 publications

A new Abel inversion algorithm by using legendre polynomials

A new Abel inversion algorithm by using legendre polynomials

Interferometric Data Analysis of Convective Heat Transfer under a Downward-Facing Horizontal Circular Plate

Evaluation of the Abel inversion integral in O-mode plasma reflectometry using Chebyshev–Gauss quadrature

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