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We present explicit filtration/backprojection-type formulae for the inversionof the spherical (circular) mean transform with the centers lying on theboundary of some polyhedra (or polygons, in 2D). The formulae are derived usingthe double layer potentials for the wave equation, for the domains with certainsymmetries. The formulae are valid for a rectangle and certain triangles in 2D,and for a cuboid, certain right prisms and a certain pyramid in 3D. All thepresent inversion formulae yield exact reconstruction within the domainsurrounded by the acquisition surface even in the presence of exterior sources.

Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra