In this work we present a method for retrieving global magnetospheric ion distributions from energetic neutral atom measurements made by the IMAGE/HENA instrument. The technique itself is based on the well-established method of constrained linear inversion. In addition to presenting the technique itself, we present a self-consistent method for its optimization. The combination of the technique itself and the tuning process provides a direct measure of the fidelity of the resulting retrievals. We apply these techniques to a representative HENA image and show that the retrieval indeed quantifies the global magnetospheric ion distributions.