Inversion of spherical means using geometric inversion and Radon transforms

We consider the problem of reconstmcting a continuous function on R" from certain values of its spherical means. A novel aspect of our approach is the use of geometric inversion to recast the inverse spherical mean problem as an inverse Radon transform problem. W define WO spherical mean inverse problems the entire problem and the causal problem. We then present a dual filtered backprojection algolithm far the entire problem and an invariant imbedding algorithm for the causal problem. We then show how geometric inversion can be used to transform the entire and causal problems into mmplete and exterior inverse Radon llansform problems, respectively. We also consider the uniqueness problem, for which we prove a sufficiency theorem and we note an application of these results Io dirraclion tomography.