The work described in this thesis is focused on the characterization and optimization of a single-phaseliquid xenon Compton camera for medical imaging applications. The detector has been conceived to exploit the advantages of an innovative medical imaging technique called 3γ imaging, which aims to obtain aprecise 3D location of a radioactive source with high sensitivity and an important reduction of the dose administered to the patient. The 3γ imaging technique is based on the detection in coincidence of 3gamma rays emitted by a specific (+β, γ) emitter radionuclide,the 44Sc. A first prototype of a liquid xenon Compton camera has been developed by Subatech laboratory within the XEMIS (Xenon Medical Imaging System) project, to proof the feas...