The universal back-projection formula for spherical means and the wave equation on certain quadric hypersurfaces

In many tomographic applications and elsewhere, there arises a need to reconstruct a function from the data on the boundary of some domain given either by the spherical means of the function, or by the corresponding solution of the free-space wave equation. In this paper, we show that the so-called universal back-projection formulas provide exact recovery of the unknown function with compact support for data on any quadric hypersurfaces that can be approximated by elliptic hypersurfaces. These quadric hypersurfaces include elliptic paraboloid as well as parabolic and elliptic cylinders.