  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 centers 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 centers of the
integration spheres) lie on a surface of a cube. This algorithm reconsrtucts
3-D images thousands times faster than backprojection-type methods.
