Remarks on the general Funk-Radon transform and thermoacoustic tomography

Preprint

7 January 2007

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0701204

Abstract

We study properties of the general integral transform defined for a family of hypersurfaces in a smooth manifold. Estimates of Sobolev norms, range conditions and approximation theorem for the kernel of the integral transform are stated. Applications to the spherical mean transform that appears in thermo/opto/photoacoustic tomography are discussed.

Keywords

THERMOACOUSTIC TOMOGRAPHY
INTEGRAL TRANSFORM
RADON TRANSFORM
GENERAL FUNK
FUNK RADON
TOMOGRAPHY

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Version 1, 2007-01-07, ArXiv

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