Analytical reconstruction formula for nn-dimensional conical Radon transform

In recent years, Radon type transforms that integrate functions along families of curves or surfaces, have been intensively studied due to their applications to inverse scattering, synthetic aperture radar (SAR), imaging science, nuclear industry, etc. In this paper, we consider the transform that integrates a function f(x)f(x) in RnRn over a family of cones invariant to translation. A new exact inversion formula is presented in the case of fixed opening angle and vertical central axis. In addition, the results of numerical simulations are presented for the case n=2n=2.