### Abstract

An explicit series solution is proposed for the inversion of the spherical mean Radon transform. Such an inversion is required in problems of thermo- and photo-acoustic tomography. Closed-form inversion formulae are currently known only for the case when the centres of the integration spheres lie on a sphere surrounding the support of the unknown function, or on certain unbounded surfaces. Our approach results in an explicit series solution for any closed measuring surface surrounding a region for which the eigenfunctions of the Dirichlet Laplacian are explicitly known - such as, for example, cube, finite cylinder, half-sphere etc. In addition, we present a fast reconstruction algorithm applicable in the case when the detectors (the centres of the integration spheres) lie on a surface of a cube. This algorithm reconstructs 3D images thousands times faster than backprojection-type methods.

Original language | English (US) |
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Pages (from-to) | S11-S20 |

Journal | Inverse Problems |

Volume | 23 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1 2007 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Signal Processing
- Mathematical Physics
- Computer Science Applications
- Applied Mathematics