Inversion of spherical means using geometric inversion and Radon transforms

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Abstract
The author considers the problem of reconstructing a continuous function on Rn from certain values of its spherical means. A novel aspect of the approach is the use of geometric inversion to recast the inverse spherical mean problem as an inverse Radon transform problem. He defines two spherical mean inverse problems: the entire problem and the causal problem. He then presents a dual filtered backprojection algorithm for the entire problem and an invariant imbedding algorithm for the causal problem. He shows how geometric inversion can be used to transform the entire and causal problems into complete and exterior inverse Radon transform problems, respectively. He also considers the uniqueness problem, for which he proves a sufficiently theorem and notes an application of these results to diffraction tomography.

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