Deprecated: $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372
Explicit inversion formulae for the spherical mean Radon transform - MaRDI portal

Explicit inversion formulae for the spherical mean Radon transform

From MaRDI portal
Publication:3425212

DOI10.1088/0266-5611/23/1/021zbMath1127.44003arXivmath/0609341OpenAlexW2098405800MaRDI QIDQ3425212

Leonid A. Kunyansky

Publication date: 7 March 2007

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0609341




Related Items (69)

Range description for a spherical mean transform on spaces of constant curvatureInversion formula for a Radon-type transform arising in photoacoustic tomography with circular integrating detectorsRange descriptions for the spherical mean Radon transformDiagonal spherical meansThe spherical Radon transform with centers on cylindrical surfacesTheoretically exact photoacoustic reconstruction from spatially and temporally reduced dataRecovering functions from the spherical mean transform with limited radii data by expansion into spherical harmonicsA Novel Compressed Sensing Scheme for Photoacoustic TomographyTHERMOACOUSTIC TOMOGRAPHY AND THE CIRCULAR RADON TRANSFORM: EXACT INVERSION FORMULAMathematics of Hybrid Imaging: A Brief ReviewA Radon-type transform arising in photoacoustic tomography with circular detectors: spherical geometryInversion formulas and stability estimates of the wave operator on the hyperplaneA Dissipative Time Reversal Technique for Photoacoustic Tomography in a CavityMethod of analytic continuation for the inverse spherical mean transform in constant curvature spacesImage reconstruction from radially incomplete spherical Radon dataThe vertical slice transform on the unit spherePhotoacoustic inversion formulas using mixed data on finite time intervals*Reconstruction of the initial state from the data measured on a sphere for plasma-acoustic wave equationsInversion of the pair of weighted and classical circular Radon transforms in \(\mathcal{C}(\mathbf{R}^2)\)Mathematics of thermoacoustic tomographyExplicit Inversion Formulas for the Two-Dimensional Wave Equation from Neumann TracesIterative methods for photoacoustic tomography in attenuating acoustic mediaInverse problems of combined photoacoustic and optical coherence tomographyEllipsoidal and hyperbolic Radon transforms; microlocal properties and injectivityA Galerkin Least Squares Approach for Photoacoustic TomographyUtilizing Variational Autoencoders in the Bayesian Inverse Problem of Photoacoustic TomographyAnalysis of the Linearized Problem of Quantitative Photoacoustic TomographyEfficient regularization with wavelet sparsity constraints in photoacoustic tomographyMicrolocal analysis for spherical Radon transform: two nonstandard problemsJoint reconstruction of initial pressure distribution and spatial distribution of acoustic properties of elastic media with application to transcranial photoacoustic tomographyApproximate marginalization of unknown scattering in quantitative photoacoustic tomographyA time reversal algorithm in acoustic media with Dirac measure approximationsNumerical inversion and uniqueness of a spherical Radon transform restricted with a fixed angular spanAn inversion formula for the spherical mean transform with data on an ellipsoid in two and three dimensionsRecovering functions from the spherical mean transform with data on an ellipse using eigenfunction expansion in elliptical coordinatesA symmetric integral identity for Bessel functions with applications to integral geometryOn a reconstruction formula for spherical Radon transform: a microlocal analytic point of viewReconstruction from circular and spherical mean dataOn artifacts in limited data spherical Radon transform: curved observation surfaceIntegral Geometry and Mathematical Problems of Image ReconstructionPhotoacoustic and Thermoacoustic Tomography: Image Formation PrinciplesMathematics of Photoacoustic and Thermoacoustic TomographyRecovering finite parametric distributions and functions using the spherical mean transformAn efficient reconstruction approach for a class of dynamic imaging operatorsA Forward-Adjoint Operator Pair Based on the Elastic Wave Equation for Use in Transcranial Photoacoustic Computed TomographyTo local reconstruction from the spherical mean Radon transformFREQUENCY DOMAIN RECONSTRUCTION FOR PHOTO- AND THERMOACOUSTIC TOMOGRAPHY WITH LINE DETECTORSOperator learning approach for the limited view problem in photoacoustic tomographyOrthogonal function series formulas for inversion of the spherical Radon transformRecovery of pressure and wave speed for photoacoustic imaging under a condition of relative uncertaintyRecovering the Initial Data of the Wave Equation from Neumann TracesPhotoacoustic Imaging for Attenuating Acoustic MediaAttenuation Models in PhotoacousticsDirect quantitative photoacoustic tomography for realistic acoustic mediaMathematical methods in biomedical imagingImage Reconstruction in Quantitative Photoacoustic Tomography with the Simplified $P_2$ ApproximationPhotoacoustic tomography with direction dependent data: an exact series reconstruction approachReconstruction algorithms for photoacoustic tomography in heterogeneous damping mediaDeep learning for photoacoustic tomography from sparse dataTo recovering the moments from the spherical mean Radon transformA new version of the quasi-reversibility method for the thermoacoustic tomography and a coefficient inverse problemRecovering a Function from Circular Means or Wave Data on the Boundary of Parabolic DomainsArtifacts in Incomplete Data Tomography with Applications to Photoacoustic Tomography and SonarThe universal back-projection formula for spherical means and the wave equation on certain quadric hypersurfacesAn algorithm for total variation regularized photoacoustic imagingMotion Estimation and Correction in Photoacoustic Tomographic ReconstructionAnalysis of Iterative Methods in Photoacoustic Tomography with Variable Sound SpeedInversion of the spherical Radon transform on spheres through the origin using the regular Radon transformOn the exactness of the universal backprojection formula for the spherical means Radon transform




This page was built for publication: Explicit inversion formulae for the spherical mean Radon transform