Recovering a Function from Circular Means or Wave Data on the Boundary of Parabolic Domains

DOI10.1137/140960219zbMath1315.65107OpenAlexW2079678077MaRDI QIDQ5250007

Sergiy jun. Pereverzyev, Markus Haltmeier

Publication date: 15 May 2015

Published in: SIAM Journal on Imaging Sciences (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/00438e06002fe23351b19cf4d3be977527eaf980

zbMATH Keywords

wave equationRadon transformnumerical examplesmedical imaginginversion formularemote sensingparabolic domaincircular meansphotoacoustic tomographyuniversal back-projectiondynamic aperture length correctionweight factor correction

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Wave equation (35L05) Radon transform (44A12) Numerical methods for integral transforms (65R10) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Numerical methods for inverse problems for integral equations (65R32)

Related Items (9)

The spherical Radon transform with centers on cylindrical surfaces ⋮ Theoretically exact photoacoustic reconstruction from spatially and temporally reduced data ⋮ Photoacoustic inversion formulas using mixed data on finite time intervals* ⋮ Explicit Inversion Formulas for the Two-Dimensional Wave Equation from Neumann Traces ⋮ A Galerkin Least Squares Approach for Photoacoustic Tomography ⋮ Operator learning approach for the limited view problem in photoacoustic tomography ⋮ Recovering the Initial Data of the Wave Equation from Neumann Traces ⋮ The universal back-projection formula for spherical means and the wave equation on certain quadric hypersurfaces ⋮ On the exactness of the universal backprojection formula for the spherical means Radon transform

Cites Work

• Unnamed Item
• Photo-acoustic inversion in convex domains
• Partial differential equations. 4th ed
• An inversion formula for the spherical mean transform with data on an ellipsoid in two and three dimensions
• On a reconstruction formula for spherical Radon transform: a microlocal analytic point of view
• The universal back-projection formula for spherical means and the wave equation on certain quadric hypersurfaces
• Inversion of circular means and the wave equation on convex planar domains
• A uniform reconstruction formula in integral geometry
• Exact reconstruction formula for the spherical mean Radon transform on ellipsoids
• Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra
• A Mollification Approach for Inverting the Spherical Mean Radon Transform
• Explicit inversion formulae for the spherical mean Radon transform
• Mathematics of thermoacoustic tomography
• Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media
• Thermoacoustic tomography with detectors on an open curve: an efficient reconstruction algorithm
• Spherical means with centers on a hyperplane in even dimensions
• FREQUENCY DOMAIN RECONSTRUCTION FOR PHOTO- AND THERMOACOUSTIC TOMOGRAPHY WITH LINE DETECTORS
• Inversion ofN-Dimensional Spherical Averages
• On the Determination of a Function from Spherical Averages
• Determining a Function from Its Mean Values Over a Family of Spheres
• Summability kernels for circular and spherical mean data
• THERMOACOUSTIC TOMOGRAPHY AND THE CIRCULAR RADON TRANSFORM: EXACT INVERSION FORMULA
• Inversion of Spherical Means and the Wave Equation in Even Dimensions
• Universal Inversion Formulas for Recovering a Function from Spherical Means
• Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed
• A series solution and a fast algorithm for the inversion of the spherical mean Radon transform
• Temporal back-projection algorithms for photoacoustic tomography with integrating line detectors
• Experimental evaluation of reconstruction algorithms for limited view photoacoustic tomography with line detectors

This page was built for publication: Recovering a Function from Circular Means or Wave Data on the Boundary of Parabolic Domains