MuST, multiples enhanced ST method for randoms rate estimations

The PET technique is based on the detection in coincidence of the two photons created in a positron annihilation. In the process of finding these pairs some accidental coincidences are obtained. These correspond to photons coming from different annihilations. Accidental coincidences, or randoms, are one of the main sources of image degradation. It is possible to partially compensate their negative impact. To this end, methods providing an estimation of the randoms present in the classified data are required. A common method of choice is the so called Singles Rate, SR. Its estimation is provided by the well known formula: R_ij = 2τS_iS_j. Since it only requires the knowledge of the singles count rates, it is simple to implement and has low statistical fluctuations. However, this method systematically overestimates the true rate and fails considerably in scenarios with inter-crystal scatter, ICS, events in the data. Which are present when the lower energy threshold is set below 255.5 keV to enhance the sensitivity of a PET scanner. For conventional energy windows, i.e. without ICS, SR can be improved by including the contributions of true coincidences, ST method. The inclusion eliminates the overestimation and provides results compatible with the correct value. Nevertheless, some (expected) disagreement was found when applying ST to scenarios with ICS, specially for non-extended sources located close to the Field-of-View, FOV, where the mismatch could be of 50%. In this work we have investigated the potential improvements that can be achieved when true triple coincidences are also taken into account, MuST method. This was done by performing several Monte Carlo simulations. Remarkably, the results show an excellent agreement with the true value regardless of the geometry of the source, the activity and the energy window considered. Except for high activities (in our particular case above 1 mCi), the agreement is always within a few- - percent, 2% at worst. We are currently investigating possible extensions that allow to obtain the MuST estimation with only measurable quantities. Which would open the door to use MuST in ICS scenarios to enhance the sensitivity of future scanners.