A numerical solution of the dynamic vector tomography problem using the truncated singular value decomposition method
type: Item
instance of: scholarly article
title: A numerical solution of the dynamic vector tomography problem using the truncated singular value decomposition method
author: Anna Petrovna Polyakova
author: I. E. Svetov
publication date: 2024-02-12T00:00:00Z
Mathematics Subject Classification ID: 65R10
Mathematics Subject Classification ID: 65R32
zbMATH DE Number: 7803167
zbMATH Keywords: dynamic vector tomography
zbMATH Keywords: longitudinal ray transform
zbMATH Keywords: transverse ray transform
zbMATH Keywords: singular value decomposition
zbMATH Keywords: orthogonal polynomial
MaRDI profile type: Publication
full work available at URL: jiip-2022-0019
OpenAlex ID: W4307282813
cites work: Representation of a Function by Its Line Integrals, with Some Radiological Applications
cites work: A singular value decomposition for the radon transform inn-dimensional euclidean space
cites work: Singular value decomposition and its application to numerical inversion for ray transforms in 2D vector tomography
cites work: Q4427974
cites work: Polynomial bases for subspaces of vector fields in the unit ball. Method of ridge functions
cites work: Numerical solvers based on the method of approximate inverse for 2D vector and 2-tensor tomography problems
cites work: Efficient algorithms for linear dynamic inverse problems with known motion
cites work: Reconstruction of dynamic objects with affine deformations in computerized tomography
cites work: Dynamic linear inverse problems with moderate movements of the object: ill-posedness and regularization
cites work: Null space and resolution in dynamic computerized tomography
cites work: Detectable Singularities from Dynamic Radon Data
cites work: An accurate approximate algorithm for motion compensation in two-dimensional tomography
cites work: Local Tomography and the Motion Estimation Problem
cites work: Singular value decomposition for the 2D fan-beam Radon transform of tensor fields
cites work: Orthogonal Function Series Expansions and the Null Space of the Radon Transform
cites work: Approximate inverse for linear and some nonlinear problems
cites work: The x-ray transform: singular value decomposition and resolution
cites work: Q4027663
cites work: Q3754464
cites work: The Singular Value Decomposition of the Operators of the Dynamic Ray Transforms Acting on 2D Vector Fields
cites work: Numerical solution of the problem of reconstructing a potential vector field in the unit ball from its normal Radon transform
cites work: Singular value decompositions and inversion methods for the exterior Radon transform and a spherical transform
cites work: The approximate inverse in action. III: 3D-Doppler tomography
cites work: Defect correction in vector field tomography: detecting the potential part of a field using BEM and implementation of the method
cites work: Integral geometry for tensor fields. Transl. from the Russian
cites work: Inversion formulas for recovering the harmonic 2D-vector field by known ray transforms
cites work: A numerical solver based on \(B\)-splines for 2D vector field tomography in a refracting medium
cites work: Comparison of two algorithms for the numerical solution of the two-dimensional vector tomography
DOI: 10.1515/JIIP-2022-0019
published in: Journal of Inverse and Ill-posed Problems
description: scientific article; zbMATH DE number 7803167