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Since the seventies, positron emission tomography (PET) has become an invaluable medical molecular imaging modality with an unprecedented sensitivity at the picomolar level, especially for cancer diagnosis and the monitoring of its response to therapy. More recently, its combination with x-ray computed tomography (CT) or magnetic resonance (MR) has added high precision anatomic information in fused PET/CT and PET/MR images, thus compensating for the modest intrinsic spatial resolution of PET. Nevertheless, a number of medical challenges call for further improvements in PET sensitivity. These concern in particular new treatment opportunities in the context personalized (also called precision) medicine, such as the need to dynamically track a small number of cells in cancer immunotherapy or stem cells for tissue repair procedures. A better signal-to-noise ratio (SNR) in the image would allow detecting smaller size tumours together with a better staging of the patients, thus increasing the chances of putting cancer in complete remission. Moreover, there is an increasing demand for reducing the radioactive doses injected to the patients without impairing image quality.