Explicit inversion formulas for the spherical mean Radon transform
| dc.creator | Kunyansky, L. | |
| dc.date | 2006-09-13 | |
| dc.date | 2006-10-25 | |
| dc.date.accessioned | 2026-07-07T07:24:46Z | |
| dc.date.available | 2026-07-07T07:24:46Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0609341 | |
| dc.identifier | http://arxiv.org/abs/math/0609341 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116489 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 44A12, 92C55, 65R32 | |
| dc.title | Explicit inversion formulas for the spherical mean Radon transform | |
| dc.type | text |