Improved random coincidence estimation including triple coincidence detection in PET

Coincidence detection in PET is inherently prone to misidentification due to the presence of randomly occurring singles from different decays within the coincidence time window. Random triple coincidences, arising when three singles from at least two decays are detected within this window, can lead to bias by acceptance without further consideration in the double coincidence identification, or result in sensitivity loss if rejected. True triple coincidences, which occur with ${\beta }^{+}\text{-}\gamma$ -emitters used in dual-tracer PET and positronium lifetime imaging, are also affected by random coincidences, leading to errors that necessitate appropriate correction. The aim of this work was to develop an accurate method for estimating random double and triple coincidences which is crucial for quantitative PET imaging of ${\beta }^{+}-$ and ${\beta }^{+}\text{-}\gamma$ -emitters. The number of random triple coincidences was evaluated for both emitter types. To process double and triple coincidences separately, coincidence identification schemes were defined with intervals free of other singles as vetoes for accepted coincidences. Random coincidences were estimated using extended delayed window techniques, which match the interval sizes for coincidence windows and vetoes. Coincidences comprising singles from two and three decays were separated in simulation studies, and two delayed windows were applied to guarantee the singles' independence in the latter case. Correction factors from additional coincidence identification schemes were used to compensate for differences in the total veto interval size between the prompt and delayed methods. The methods were evaluated using simulations for different isotopes, coincidence windows, phantom shapes, and activities. The simulation results were then validated against measurements obtained with a brain PET scanner. The total random coincidence rate for the entire scanner was estimated with a relative deviation of <3% for double coincidences and <5% for triple coincidences of two decays of ${\beta }^{+}$ -emitters and ${\beta }^{+}\text{-}\gamma$ -emitters for the investigated coincidence identification schemes and for the simulated cases.