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.
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Leonid Kunyansky (2007) studied this question.
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