The cone beam transform of a tensor field of orderminn≥2dimensions is considered. We prove that the image of a tensor field under this transform is related to a derivative of then-dimensional Radon transform applied to a projection of the tensor field. Actually the relation we show reduces form=0andn=3to the well-known formula of Grangeat. In that sense, the paper contains a generalization of Grangeat's formula to arbitrary tensor fields in any dimension. We further briefly explain the importance of that formula for the problem of tensor field tomography. Unfortunately, form>0, an inversion method cannot be derived immediately. Thus, we point out the possibility to calculate reconstruction kernels for the cone beam transform using Grangeat's formula.
A weighted de Rham operator acting on arbitrary tensor fields and their local potentials
