In positron emission tomography (PET), the annihilation radiation is usually detected as a coincidence occurrence that localizes the position of the annihilation event to a straight line joining the detectors. The measure of the difference between the time of flight (TOF) of the annihilation photons between their inception and their detection permits the localization of the position of the annihilation event along the coincidence line. The incorporation of TOF information into the PET reconstruction process improves the signal-to-noise ratio in the image obtained. The utilization of scintillation detectors utilizing cesium fluoride scintillators, fast photomultiplier tubes, and fast timing circuits allows sub-nanosecond coincidence timing resolution needed for the effective use of TOF in PET. Mathematical considerations and pilot experiments show that with state-of-the-art electronic components and through the application of proper reconstruction algorithms, the combination of TOF and PET positional data improves severalfold the signal-to-noise ratio with respect to conventional PET image reconstruction at the cost of increasing the amount of data to be processed. The construction of a TOF-assisted PET device is within the capability of state-of-the-art technology.