A series inversion for the x-ray transform in n dimensions

Abstract

An inversion for the x-ray transform in Rn is given for square integrable functions supported in the unit ball E. An orthonormal basis for L2(E) is described in terms of spherical harmonics and Jacobi polynomials and the inversion is done in terms of the generalised Fourier series expansion with respect to that basis. The result is derived by using the projection slice theorem to show that the X-ray transform is block diagonal with respect to the above basis for L2(E) and the transform of that basis along a fixed direction omega 0.