Orthogonal Function Series Expansions and the Null Space of the Radon Transform

From MaRDI portal
Publication:3315975

DOI10.1137/0515047zbMath0533.42018OpenAlexW1963604045MaRDI QIDQ3315975

Alfred K. Louis

Publication date: 1984

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0515047



Related Items

New range theorems for the dual Radon transform, A range characterization of the single-quadrant ADRT, Polynomial bases for subspaces of vector fields in the unit ball. Method of ridge functions, Singular value decomposition of a normal Radon transform operator acting on 3D symmetric 2-tensor fields, The C∞ -isomorphism property for a class of singularly-weighted x-ray transforms, 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, Biorthogonal decompositions of the Radon transform by multivariate interpolation, The cone-beam transform and spherical convolution operators, The spherical tensor approach to 3D tensor field tomography, Singular value decomposition for longitudinal, transverse and mixed ray transforms of 2D tensor fields, Singular Value Decomposition of the Wave Forward Operator with Radial Variable Coefficients, Higher-rank Radon transforms on constant curvature spaces, Radon needlet thresholding, A numerical solution of the dynamic vector tomography problem using the truncated singular value decomposition method, The method of approximate inverse for the Radon transform operator acting on functions and for the normal Radon transform operators acting on vector and symmetric 2-tensor fields in \(\mathbb R^3\), Functional Relations, Sharp Mapping Properties, and Regularization of the X-Ray Transform on Disks of Constant Curvature, Efficient nonparametric Bayesian inference for \(X\)-ray transforms, Two approaches to the problem of defect correction in vector field tomography solving boundary value problems, Reconstruction of a Vector Field in a Ball from its Normal Radon Transform, Singular value decomposition and its application to numerical inversion for ray transforms in 2D vector tomography, Asymptotic inversion formulas in 3D vector field tomography for different geometries, Null space and resolution in dynamic computerized tomography, Orthogonal function series formulae for inversion of the conical Radon transform with a fixed central axis, Design and processing of invertible orientation scores of 3D images, Singular value decomposition of the attenuated conical Radon transform with a fixed central axis and opening angle, Orthogonal function series formulas for inversion of the spherical Radon transform, Die Wirkung der Radon-Transformation auf Polynomräume. (The effect of the Radon-transform to polynomial spaces), Range characterizations and singular value decomposition of the geodesic X-ray transform on disks of constant curvature, Singular value decomposition of the longitudinal ray transform of vector fields in a ball in cone beam coordinates, Generalized disk polynomial via Laplace integral representation, Inversion of noisy Radon transform by SVD based needlets, Commuting integral and differential operators and the master symmetries of the Korteweg–de Vries equation, Nonuniqueness in inverse Radon problems: The frequency distribution of the ghosts, Euclidean motion group representations and the singular value decomposition of the Radon transform, On linear spline algorithms of computerized tomography in the space of \(n\)-orbits, Incomplete data problems in x-ray computerized tomography, A Remez-type algorithm for calculation of extremal fundamental systems for polynomial spaces on the sphere