Resolution enhancement in PET reconstruction using collimation

Collimation can improve both the spatial resolution and sampling properties compared to the same scanner without collimation. Spatial resolution improves because each original crystal can be conceptually split into two (i.e., a right and left half) by masking half the crystal with a high-density attenuator (e.g., tungsten); this reduces efficiency by 4x since both crystals comprising the line of response (LOR) are masked, but yields 4x as many resolution-enhanced (RE) LORs. All the new RE LORs can be measured by scanning with the collimator in different configurations. In this simulation study, which is leading to the fabrication of a prototype collimator, the collimator was assumed to be ideal, neither allowing gamma penetration nor truncating the field of view. Comparisons were made in 2D between an uncollimated small-animal system with 2-mm ideal crystals that were perfectly absorbing and the same system with collimation that narrowed the effective crystal size to 1 mm. Digital phantoms included a hot-rod and a point source, both in a uniform background with contrast of 3:1. In addition to the collimated and uncollimated configurations, angular and spatial wobbling acquisitions of the 2-mm case were also simulated. Similarly, simulations with different combinations of the RE LORs were considered including (i) all 4x, (ii) only those parallel to the 2-mm LORs; and (iii) only cross pairs that are not parallel. Lastly, simulations of mixing collimated and uncollimated data were conducted. The reconstructions show that for most noise levels there is a substantial improvement in image quality by using collimation even when there are 4x fewer counts. In many cases, the noisy reconstructions are superior in resolution to even the noiseless uncollimated reconstructions. By comparing various configurations of sampling, the results show that it is the matched combination of both improved spatial resolution of each LOR and the increase in the number of LORs that yields imp- oved reconstructions.