Inversion ofN-Dimensional Spherical Averages

In this paper, we give a simple inversion formula for determining the even part of a function from its averages over the surfaces of spheres in Rⁿ, centered on a hyperplane $y = 0$. We emphasize the relation between the backprojection approximation to the function and the full inversion result. A simple necessary and sufficient condition for data to correspond to the spherical averages of a function is given.