  Positron emission tomography, like many other tomographic imaging modalities,
relies on an image reconstruction step to produce cross-sectional images from
projection data. Detection and localization of the back-to-back annihilation
photons produced by positron-electron annihilation defines the trajectories of
these photons, which when combined with tomographic reconstruction algorithms,
permits recovery of the distribution of positron-emitting radionuclides. Here
we produce cross-sectional images directly from the detected coincident
annihilation photons, without using a reconstruction algorithm. Ultra-fast
radiation detectors with a resolving time averaging 32 picoseconds measured the
difference in arrival time of pairs of annihilation photons, localizing the
annihilation site to 4.8 mm. This is sufficient to directly generate an image
without reconstruction and without the geometric and sampling constraints that
normally present for tomographic imaging systems.
