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In the present work, the Neural Networks (NNs) are used to reconstruct the interaction point of an event producing a signal shared among different photodetector in a conventional Anger Camera. The event is caused by the interaction of a medium-high energy gamma ray within a scintillator crystal coupled with Silicon Drift Detectors (SDDs). Two different energy ranges are considered for the incident gamma ray: 122-140 keV and 1.1 MeV. In the first one (122-140 keV), the Photoelectric Effect is dominant over the Compton Effect, while in the second one (1.1 MeV) the situation is the opposite and the Pair Production Effect may still be ignored. At low energies, it is shown that the NNs obtain results in simulations and with experimental data comparable or better than other methods, like the Centroid (CM) and the Maximum Likelihood (ML) ones, and a precision lower than 1 mm at low noise levels (for an Equivalent Noise Charge -ENC- less than 20e-). At high energies, the NNs maintain a good precision, even in the occurrence of Compton interactions, with a spatial resolution of approximately 2.1 mm. Finally, the possibility to obtain the second interaction point position when a Compton Scattering occurs is examined and first simulations are presented.