In this article, we propose a novel image reconstruction technique for three-gamma (3-<inline-formula> <tex-math notation="LaTeX"> {\gamma } </tex-math></inline-formula>) imaging systems that aims at reaching high image quality with a low statistics. The proposed approach is based on the utilization of a (<inline-formula> <tex-math notation="LaTeX"> {\beta +} </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">{\gamma } </tex-math></inline-formula>) emitter and a liquid xenon (LXe) camera, the Xenon Medical Imaging System 2 (XEMIS2), that is currently being manufactured. The third gamma emitted is more energetic than the two 511-keV photons and interacts mostly through Compton scattering in LXE; therefore, we utilize the interactions' position and the deposited energy to define a Compton cone that gives the direction from where the third gamma was emitted. The intersection point between the cone and the two coincidence photons' lines of response (LOR) is the center of the probability distribution function (PDF), a resolution model similar to that of time-of-flight (TOF)-positron emission tomography (PET). The third gamma's information is used to narrow the LOR portion employed during reconstruction. In this article, we show reconstruction results from simulation using highly realistic Geant4 Application for Emission Tomography (GATE) Monte Carlo simulation of the imaging device and a NEMA-like phantom.