Fast reconstruction algorithms for the thermoacoustic tomography in certain domains with cylindrical or spherical symmetries

DOI10.3934/ipi.2012.6.111zbMath1241.65079arXiv1102.1413OpenAlexW2053026187MaRDI QIDQ2428064

Leonid A. Kunyansky

Publication date: 24 April 2012

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

Full work available at URL: https://arxiv.org/abs/1102.1413

zbMATH Keywords

wave equationinverse problemfinite difference methodRadon transformnumerical examplesfast algorithmsintegral equation methodspherical meansinversion algorithmthermoacoustic tomographyintegrating detectorsreconstructions from real measurements

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Inverse problems for PDEs (35R30) Wave equation (35L05) Radon transform (44A12) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical methods for integral transforms (65R10) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Boundary element methods for initial value and initial-boundary value problems involving PDEs (65M38)

Related Items (12)

The spherical Radon transform with centers on cylindrical surfaces ⋮ Theoretically exact photoacoustic reconstruction from spatially and temporally reduced data ⋮ Inversion formulas and stability estimates of the wave operator on the hyperplane ⋮ Reconstruction of the initial state from the data measured on a sphere for plasma-acoustic wave equations ⋮ Singular Value Decomposition of the Wave Forward Operator with Radial Variable Coefficients ⋮ Reconstruction formula for photoacoustic tomography with cylindrical detectors ⋮ Microlocally accurate solution of the inverse source problem of thermoacoustic tomography ⋮ Reconstruction of the initial function from the solution of the fractional wave equation measured in two geometric settings ⋮ Exterior/interior problem for the circular means transform with applications to intravascular imaging ⋮ Photoacoustic tomography with line detector: exact inversion formula ⋮ Orthogonal function series formulas for inversion of the spherical Radon transform ⋮ Inversion of the spherical Radon transform on spheres through the origin using the regular Radon transform

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