Explicit inversion formulas for the spherical mean Radon transform
Analysis of PDEs
2007-05-23 v2
Abstract
We derive explicit formulas for the reconstruction of a function from its integrals over a family of spheres, or for the inversion of the spherical mean Radon transform. Such formulas are important for problems of thermo- and photo- acoustic tomography. A closed-form inversion formula of a filtration-backprojection type is found for the case when the centers of the integration spheres lie on a sphere in Rn surrounding the support of the unknown function. An explicit series solution is presented for the case when the centers of the integration spheres lie on a general closed surface.
Cite
@article{arxiv.math/0609341,
title = {Explicit inversion formulas for the spherical mean Radon transform},
author = {L. Kunyansky},
journal= {arXiv preprint arXiv:math/0609341},
year = {2007}
}