  Inversion of Radon transforms is the mathematical foundation of many modern
tomographic imaging modalities. In this paper we study a conical Radon
transform, which is important for computed tomography taking Compton scattering
into account. The conical Radon transform we study integrates a function in
$\R^d$ over all conical surfaces having vertices on a hyperplane and symmetry
axis orthogonal to this plane. As the main result we derive exact
reconstruction formulas of the filtered back-projection type for inverting this
transform.
