Singular value decomposition and its application to numerical inversion for ray transforms in 2D vector tomography

DOI10.1515/jiip.2011.047zbMath1279.33015OpenAlexW2123006997MaRDI QIDQ5745481

Alfred K. Louis, Thomas Schuster, Anton V. Efimov, E. Yu. Derevtsov

Publication date: 30 January 2014

Published in: jiip (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jiip.2011.047

zbMATH Keywords

orthogonal polynomialsRadon transformsingular value decompositionvector fieldray transformvector tomography

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Numerical methods for integral transforms (65R10) Numerical methods for inverse problems for integral equations (65R32)

Related Items

Numerical solution of the problem of reconstructing a potential vector field in the unit ball from its normal Radon transform, The localized basis functions for scalar and vector 3D tomography and their ray transforms, Inversion formulae for ray transforms in vector and tensor tomography, Singular value decomposition for longitudinal, transverse and mixed ray transforms of 2D tensor fields, Weighted Radon transforms of vector fields, with applications to magnetoacoustoelectric tomography, Inversion of generalized Radon transforms acting on 3D vector and symmetric tensor fields, A numerical solution of the dynamic vector tomography problem using the truncated singular value decomposition method, 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, Vectorial Slepian Functions on the Ball, Reconstruction of a Vector Field in a Ball from its Normal Radon Transform, The Method of Approximate Inverse for Ray Transform Operators on Two-Dimensional Symmetric m-Tensor Fields, Solving inverse problems using data-driven models, Range characterizations and singular value decomposition of the geodesic X-ray transform on disks of constant curvature, Well-defined forward operators in dynamic diffractive tensor tomography using viscosity solutions of transport equations

Cites Work

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