Reconstruction of a Vector Field in a Ball from its Normal Radon Transform

DOI10.1007/S10958-015-2256-1zbMath1349.65731OpenAlexW2147097328MaRDI QIDQ5741339

Anna Petrovna Polyakova

Publication date: 22 July 2016

Published in: Journal of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-015-2256-1

zbMATH Keywords

singular value decompositionorthogonal polynomialpotential fieldvector tomographynormal Radon transform

Mathematics Subject Classification ID

Radon transform (44A12) Numerical methods for integral transforms (65R10) Numerical methods for inverse problems for integral equations (65R32)

Related Items (5)

Numerical solution of the problem of reconstructing a potential vector field in the unit ball from its normal Radon transform ⋮ Weighted Radon transforms of vector fields, with applications to magnetoacoustoelectric tomography ⋮ Inversion of generalized Radon transforms acting on 3D vector and symmetric tensor fields ⋮ The Singular Value Decomposition of the Operators of the Dynamic Ray Transforms Acting on 2D Vector Fields ⋮ The Method of Approximate Inverse in Slice-by-Slice Vector Tomography Problems

Cites Work

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• The method of orthogonal projection in potential theory
• Orthogonal Function Series Expansions and the Null Space of the Radon Transform
• Singular value decomposition for the 2D fan-beam Radon transform of tensor fields
• Singular value decomposition and its application to numerical inversion for ray transforms in 2D vector tomography

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