The Radon transform.
From MaRDI portal
Publication:1292931
zbMath0932.43011MaRDI QIDQ1292931
Publication date: 9 August 1999
Published in: Progress in Mathematics (Search for Journal in Brave)
Harmonic analysis on homogeneous spaces (43A85) Radon transform (44A12) Analysis on other specific Lie groups (43A80) Research exposition (monographs, survey articles) pertaining to integral transforms (44-02)
Related Items
Injectivity of rotation invariant windowed Radon transforms, Directional short-time Fourier transform of distributions, Generalizations of the Busemann-Petty problem for sections of convex bodies, Reconstruction of functions from their integrals over \(k\)-planes, Deep microlocal reconstruction for limited-angle tomography, \(q\)-deformed Morse and oscillator potential, Weakly-singular, weak-form integral equations for cracks in three-dimensional anisotropic media, The Gaussian limit for high-dimensional spherical means, A stereoscopic look into the bulk, Gelfand transforms of \(\mathrm{SO}(3)\)-invariant Schwartz functions on the free group \(N_{3,2}\), Kernel-based methods for inversion of the Radon transform on SO(3) and their applications to texture analysis, Higher-rank wavelet transforms, ridgelet transforms, and Radon transforms on the space of matrices, Efficient tensor tomography in Fan-beam coordinates, Reconstructing a function on the sphere from its means along vertical slices, The Abel, Fourier and Radon transforms on symmetric spaces, Model-based reconstruction for magnetic particle imaging in 2D and 3D, Ray transform on Sobolev spaces of symmetric tensor fields. I: Higher order Reshetnyak formulas, Generalized intersection bodies, A negative answer to Ulam's problem 19 from the Scottish Book, Inversion of the attenuated X-ray transforms: method of Riesz potentials, Spectral theorems associated with the directional short-time Fourier transform, Support theorem for the light-ray transform of vector fields on Minkowski spaces, Singular self-dual Zollfrei metrics and twistor correspondence, On functions with given spherical means on symmetric spaces, Busemann-Petty problems for quasi \(L_p\) intersection bodies, Directional short-time Fourier transform, A trace formula for long-range perturbations of the Landau Hamiltonian, Explicit inversion formulas for the \(X\)-ray transform in \(\mathbb{Z}^n\), A generalized Radon transform on the plane, An uncertainty principle of Paley and Wiener on Euclidean motion group, Equivalent equations of motion for gravity and entropy, Radon needlet thresholding, Boundary kinematic space, The Penrose transform in split signature, Symmetric subvarieties in compactifications and the Radon transform on Riemannian symmetric spaces of noncompact type., Asymptotic density of eigenvalue clusters for the perturbed Landau Hamiltonian, Analysis of fractures in 3D piezoelectric media by a weakly singular integral equation method, Weakly singular integral equations for Darcy's flow in anisotropic porous media, Vector tomography for reconstructing electric fields with non-zero divergence in bounded domains, Gauge equivalence and inverse scattering for long-range magnetic potentials, Stability estimates for the Radon transform with restricted data and applications, The Radon transform on the Heisenberg group and the transversal Radon transform, The sphere method for the inverse problems of the Radon transforms, High-velocity estimates for the scattering operator and Aharonov-Bohm effect in three dimensions, Gabor frames and directional time-frequency analysis, Multi-scale texture modeling, Fourier transform and related integral transforms in superspace, Non-smooth unobservable states in control problem for the wave equation in \(\mathbb{R}^3\), Radon transform on the torus, Generalized splines for Radon transform on compact Lie groups with applications to crystallography, Efficient nonparametric Bayesian inference for \(X\)-ray transforms, Semyanistyi's integrals and Radon transforms on matrix spaces, Regularization in a functional reproducing kernel Hilbert space, Unitarization of the horocyclic Radon transform on homogeneous trees, On bodies with directly congruent projections and sections, Image reconstruction from scattered Radon data by weighted positive definite kernel functions, Full reconstruction of a vector field from restricted Doppler and first integral moment transforms in \(\mathbb{R}^n\), A local support theorem for the radiation fields on asymptotically Euclidean manifolds, Inversion of the local Pompeiu transformation on Riemannian symmetric spaces of rank one, The dual of non-extremal area: differential entropy in higher dimensions, Toeplitz operators for wavelet transform related to the spherical mean operator, Notes on a slice distance for singular \(L^p\)-bundles, On the continual Rubik's cube, A nonsplit sum of coefficients of modular forms, Weighted estimates for the \(k\)-plane transform of radial functions on Euclidean spaces, Scattered data interpolation of Radon data, C\(^*\)-algebraic intertwiners for degenerate principal series of special linear groups, Szegö-Radon transform for biaxially monogenic functions, Injectivity and stability for a generic class of generalized Radon transforms, Around theorems of Ingham-type regarding decay of Fourier transform on \(\mathbb{R}^n, \mathbb{T}^n\) and two step nilpotent Lie groups, An integral transform on a cylinder and the twistor correspondence, The Hardy-Littlewood operator associated with the Riemann-Liouville transform, Radon transform on Sobolev spaces, Inversion of the attenuated X-ray transforms -- method of convolution-backprojection, A geometric based preprocessing for weighted ray transforms with applications in SPECT, A note on the norm of an algorithm for reconstruction from Radon data on the ball, Tomographic image reconstruction based on generalized projections, Tensor tomography: progress and challenges, Radiation fields on Schwarzschild spacetime, A theoretical study of the algorithm to practicalize CT by G. N. Hounsfield and its applications, Modified Radon transform inversion using moments, The Schatten-von Neumann class associated with the Gabor-Riemann-Liouville operator, The ray transform of symmetric tensor fields with incomplete projection data. I: The kernel of the ray transform, Saturation rates of filtered back projection approximations, An inversion formula for the transport equation in \(\mathbb{R}^{3}\) using complex analysis in several variables, Convolution-backprojection method for the \(k\)-plane transform, and Calderón's identity for ridgelet transforms, Partial inversion of the 2D attenuated \(X\)-ray transform with data on an arc, \(L^p\) regularity estimates for a class of integral operators with fold blowdown singularities, Integral geometry on discrete Grassmannians in \(\mathbb{Z}^n\), Range characterizations and singular value decomposition of the geodesic X-ray transform on disks of constant curvature, The Busemann-Petty problem on entropy of log-concave functions, Fourier analysis of periodic Radon transforms, Radon, cosine and sine transforms on real hyperbolic space, An exact Radon formula for Lambertian tomography, Understanding neural networks with reproducing kernel Banach spaces, Sonine-Dimovski transform and spectral synthesis associated with the hyper-Bessel operator on the complex plane, Inversion formulas for the spherical Radon transform and the generalized cosine transform., Exploring de Sitter space and holography, Uniqueness of extremizers for an endpoint inequality of the \(k\)-plane transform, Radiation fields, scattering, and inverse scattering on asymptotically hyperbolic manifolds, Flett potentials associated with differential-difference Laplace operators, Quantum tomographic Aubry–Mather theory, Resolution of 2 Dimensional Reconstruction of Functions with Nonsmooth Edges from Discrete Radon Transform Data, Renormalized energy of a dislocation loop in a 3D anisotropic body, Comparison problems for Radon transforms, The Radon transform with finitely many angles *, A uniqueness result for the inverse problem of identifying boundaries from weighted Radon transform, Continuity properties of the shearlet transform and the shearlet synthesis operator on the Lizorkin type spaces, Explicit representations for Banach subspaces of Lizorkin distributions, Weighted Radon transforms of vector fields, with applications to magnetoacoustoelectric tomography, Concentration close to the cone for linear waves, Carleman estimates for geodesic X-ray transforms, Inversion of generalized Radon transforms acting on 3D vector and symmetric tensor fields, Remarks on the linear wave equation, Integral representations of shallow neural network with Rectified Power Unit activation function, Nonselfadjoint Perturbations of Selfadjoint Operators in Two Dimensions II. Vanishing Averages, The windowed Fourier transform and Gabor multipliers associated with the Riemann-Liouvlle transform, The Lower Dimensional Busemann‐Petty Problem with Weights, Uncertainty principle in terms of entropy for the Riemann-Liouville operator, A one-dimensional Radon transform onSO(3) and its application to texture goniometry, A Direct Sampling Method for the Inversion of the Radon Transform, On the exactness of the universal backprojection formula for the spherical means Radon transform, A range characterization of the single-quadrant ADRT, A characterization of inverse Radon transform on the Laguerre hypergroup, Moment conditions and support theorems for Radon transforms on affine Grassmann manifolds, Radon transform on real, complex, and quaternionic Grassmannians, Inversion of the Radon transform on the product Laguerre hypergroup by using generalized wavelets, Helgason-Marchaud inversion formulas for Radon transforms, Electron Tomography and Multiscale Biology, High‐energy and smoothness asymptotic expansion of the scattering amplitude for the Dirac equation and application, Cross $i$-sections of star bodies and dual mixed volumes, Identities among Euclidean sonar and Radon transforms, Funk-Minkowski transform and spherical convolution of Hilbert type in reconstructing functions on the sphere, Lower bounds for ranks of elliptic curves, The C∞ -isomorphism property for a class of singularly-weighted x-ray transforms, Comparison of volumes of convex bodies in real, complex, and quaternionic spaces, Radon transforms on affine Grassmannians, Dual Radon transforms on affine Grassmann manifolds, Exact Inversion of the Cone Transform Arising in an Application of a Compton Camera Consisting of Line Detectors, Error estimates and convergence rates for filtered back projection, The lower dimensional Busemann-Petty problem for bodies with the generalized axial symmetry, On the radial derivative of the delta distribution, On the rigidity from infinity for nonlinear Alfvén waves, A simple shearlet-based 2D Radon inversion with an application to computed tomography, On semilinear Tricomi equations with critical exponents or in two space dimensions, An efficient algorithm to compute the X-ray transform, Time-frequency concentration and localization operators associated with the directional short-time Fourier transform, Numerical Measure of a Complex Matrix, Support theorems for the light ray transform on analytic Lorentzian manifolds, Kernels with prescribed surface tension \& mobility for threshold dynamics schemes, Intersection bodies and generalized cosine transforms, Papoulis' sampling theorem: revisited, Radial and Angular Derivatives of Distributions, Convex geometry and its applications. Abstracts from the workshop held December 12--18, 2021 (hybrid meeting), Rotation Invariant Ultradistributions, Automatic alignment for three-dimensional tomographic reconstruction, On the range of the \(X\)-ray transform of symmetric tensors compactly supported in the plane, Torus Computed Tomography, On an αth-order fractional Radon transform and a wave type of equation, End point estimates for Radon transform of radial functions on non-Euclidean spaces, A RESULT OF PALEY AND WIENER ON DAMEK–RICCI SPACES, X-ray transform on Sobolev spaces, On the generalized Busemann-Petty problem, Threshold dynamics for anisotropic surface energies, Tensor tomography on Cartan–Hadamard manifolds, Recovery of singularities from a backscattering Born approximation for a biharmonic operator in 3D, Deep synthesis network for regularizing inverse problems, A generalized funk’s section theorem for measures, Integral geometry on discrete Grassmannians 𝔾(d, n) associated to ℤ n , The \(\overline \delta\)-theory for inverse problems associated with Schödinger operators on hyperbolic spaces, The Ridgelet transform of distributions, Correlation imaging in inverse scattering is tomography on probability distributions, Nonparametric Construction of Multivariate Kernels, Determining a magnetic Schrödinger operator from partial Cauchy data, Quasi \(L_p\)-intersection bodies, Generalized intersection bodies are not equivalent, ANALYZING THE RANDOM COEFFICIENT MODEL NONPARAMETRICALLY, An inversion formula for the dual horocyclic Radon transform on the hyperbolic plane, Static arbitrage bounds on basket option prices, Riesz potentials and integral geometry in the space of rectangular matrices, The generalized totally geodesic Radon transform and its application to texture analysis, Radiation Fields on Asymptotically Euclidean Manifolds, Gauge Equivalence and Inverse Scattering for Aharonov–Bohm Effect, On the numerical solution of the eigenvalue problem in fractional quantum mechanics, Geodesic X-ray tomography for piecewise constant functions on nontrapping manifolds, On the double windowed ridgelet transform and its inverse, Bilinear identities involving thek-plane transform and Fourier extension operators, X-rays of forms and projections of currents, Busemann-Petty problems for L_p mixed intersection bodies, The Radon transform for double fibrations of semisimple symmetric spaces, Quantitative uncertainty principles associated with the directional short-time Fourier transform, Injectivity and Range Description of Integral Moment Transforms Over $m$-Tensor Fields in $\mathbb{R}^n$, Coherent Quantum Tomography, Harmonic manifolds and the volume of tubes about curves, A characterization of the inverse Radon transform associated with the classical domain of type one, Orthonormal sequences and time frequency localization related to the Riemann-Liouville operator, A possible symplectic framework for Radon-type transforms, Unnamed Item, Wave equations and the LeBrun-Mason correspondence, Unitarization and Inversion Formulae for the Radon Transform Between Dual Pairs, Trkalian fields and Radon transformation, Reconstructing the drift of a diffusion from partially observed transition probabilities, Uncertainty principles associated with the directional short-time Fourier transform, Radiation fields for semilinear wave equations, Motion reconstruction for optical tomography of trapped objects, Momentum ray transforms, II: range characterization in the Schwartz space, The Radon transform intertwines wavelets and shearlets, Book Review: Integral geometry and Radon transforms, Certain Liouville properties of eigenfunctions of elliptic operators, Sampling for the V-line transform with vertex on a circle, On the range of the attenuated Radon transform in strictly convex sets, Unnamed Item, On the Range Characterization of the Two-Dimensional Attenuated Doppler Transform, On Radon transforms on tori, An asymmetric convex body with maximal sections of constant volume, Ray transforms in hyperbolic geometry, Euclidean motion group representations and the singular value decomposition of the Radon transform, X-ray transform on a symmetric space, The geodesic ray transform on Riemannian surfaces with conjugate points, The \(d\)-plane Radon transform on the torus \(\mathbb T^n\), Analytic Inversion of a Conical Radon Transform Arising in Application of Compton Cameras on the Cylinder, Unitarization of the Horocyclic Radon Transform on Symmetric Spaces
