An improved inversion method is presented for the analysis of data obtained by imaging techniques. We apply the inversion method for the investigation of photoelectron images in order to determine the distribution of kinetic energy and emission angle of photoelectrons. The conventional inversion approach relies on an Abel-inversion formalism, valid only in a limited case of small kinetic energies of the photoelectrons. In contrast, the improved approach is valid for arbitrary kinetic energies because it explicitly accounts for the image distortion by the projection technique. The conventional and the improved approach are compared with simulated data and with measured data from photoionization of the rare gases, xenon and argon, in a strong laser field. At small energies the conventional and the new approach yield the same results, whereas for larger energies the conventional method fails but our method is still applicable. Most importantly our inversion method is applicable to arbitrary homogeneous and inhomogeneous field geometries and hence to all types of imaging spectrometers currently in use.