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.
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