Year: 2006
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Kunyansky, L.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952597014