The semi-analytical method for inversion of a weighted vector ray transform in three dimensions

DOI10.1142/S1793557120500126zbMath1425.44001OpenAlexW2883950348WikidataQ129457322 ScholiaQ129457322MaRDI QIDQ5243699

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Publication date: 19 November 2019

Published in: Asian-European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793557120500126

zbMATH Keywords

inverse problemscomputerized tomographyray transformvector spherical harmonicsspherical wave functions

Mathematics Subject Classification ID

Radon transform (44A12) Iterative numerical methods for linear systems (65F10) Numerical methods for integral transforms (65R10) Numerical methods for ill-posed problems for integral equations (65R30) Fourier series and coefficients in several variables (42B05) Numerical methods for inverse problems for integral equations (65R32)

Uses Software

• DLMF

Cites Work

• The truncated SVD as a method for regularization
• An inversion formula for the attenuated \(X\)-ray transformation
• Inversion of the attenuated Radon transform
• Mathematical Methods in Image Reconstruction
• Integrals of Products of Bessel Functions
• On the range characterization for the two-dimensional attenuated x-ray transformation
• Inverting the Attenuated Vectorial Radon Transform
• A New Type of Expansion in Radiation Problems
• Doppler tomography for vector fields
• Inversion of the scalar and vector attenuated X-ray transforms in a unit disc
• Inverse acoustic and electromagnetic scattering theory
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