PET 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 data are required. A common method of choice is the so called Singles Rate, SR. Its estimation is provided by the well known formula: Rij = 2τSiSj. 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 value. Even with conventional energy windows SR overestimates the correct rate. In this work, we improve the SR method by modeling the contribution of true coincidences and pile-up of events. The novel method, the Singles Prompt (SP), presents the same mathematical structure as SR and requires exactly the same inputs as SR. Therefore, replacing SR by SP as a randoms estimator method of choice is straightforward. We investigate the accuracy of SP in a wide range of scenarios. From point source distributions of activity to extended sources. The activities considered cover from 0.001mCi to 1mCi. We compare the performance of SP with the two most used methods: SR and Delayed Window (DW). To assess the performance of the estimation methods we need to resort to Monte-Carlo simulations. The results show that SP provides an accurate estimation of the randoms rate in all of the investigated scenarios. For conventional activities and sources, DW and SR overestimate the randoms rate by 5% and 15% while SP provides the correct value. Even in the most demanding situation (a point source of high activity) SP provides a good estimation 4% at worst, while DW and SR fail by 20% and 110% respectively.
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