SPECT imaging of prompt-gamma radiation with Compton cameras is currently investigated over the world as a relevant candidate to hadron therapy monitoring. The acquisition principle of the camera is based on Compton scattering of gamma photons on a first detector followed by absorption in the camera. The emitting point of a detected photon lies on the surface of the cone having its apex at the scattering point, the axis direction opposite to the direction of the scattered photon and the half-opening angle defined by the energies involved in the detection process. To date, several different approaches have been proposed for the modeling of the direct problem. In some models the Compton projections are integrals of the intensity of the source on conical surfaces. Weights are then given to the intensities upon the position of the point on the conical surface. In other models, the projections are the sum of the integrals of the intensity on the generatrices of the cone. Models also differ by the way they account for the measurement uncertainties. The reconstruction of the image of the source is then an important challenge which faces complexity of the model, memory load and computing time issues.