  We present a nuclear medical imaging technique, employing triple-gamma
trajectory intersections from beta^+ - gamma coincidences, able to reach
sub-millimeter spatial resolution in 3 dimensions with a reduced requirement of
reconstructed intersections per voxel compared to a conventional PET
reconstruction analysis. This '$\gamma$-PET' technique draws on specific beta^+
- decaying isotopes, simultaneously emitting an additional photon. Exploiting
the triple coincidence between the positron annihilation and the third photon,
it is possible to separate the reconstructed 'true' events from background. In
order to characterize this technique, Monte-Carlo simulations and image
reconstructions have been performed. The achievable spatial resolution has been
found to reach ca. 0.4 mm (FWHM) in each direction for the visualization of a
22Na point source. Only 40 intersections are sufficient for a reliable
sub-millimeter image reconstruction of a point source embedded in a scattering
volume of water inside a voxel volume of about 1 mm^3 ('high-resolution mode').
Moreover, starting with an injected activity of 400 MBq for ^76Br, the same
number of only about 40 reconstructed intersections are needed in case of a
larger voxel volume of 2 x 2 x 3~mm^3 ('high-sensitivity mode'). Requiring such
a low number of reconstructed events significantly reduces the required
acquisition time for image reconstruction (in the above case to about 140 s)
and thus may open up the perspective for a quasi real-time imaging.
