Abstract
We derive explicit formulae 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 formulae 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 centres of the integration spheres lie on a sphere in surrounding the support of the unknown function.
Original language | English (US) |
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Article number | 021 |
Pages (from-to) | 373-383 |
Number of pages | 11 |
Journal | Inverse Problems |
Volume | 23 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2 2007 |
ASJC Scopus subject areas
- Theoretical Computer Science
- Signal Processing
- Mathematical Physics
- Computer Science Applications
- Applied Mathematics