  The cone-beam transform consists of integrating a function defined on the
three-dimensional space along every ray that starts on a certain scanning set.
Based on Grangeat's formula, Louis [2016, Inverse Problems 32 115005] states
reconstruction formulas based on a new generalized Funk-Radon transform on the
sphere. In this article, we give a singular value decomposition of this
generalized Funk-Radon transform. We use this result to derive a singular value
decomposition of the cone-beam transform with sources on the sphere thus
generalizing a result of Kazantsev [2015, J. Inverse Ill-Posed Probl.
23(2):173-185].
