KAHIBARO
28.7. Random Events
Table of Contents
Identifying random coincidences
Random coincidences are coincidence events that occur when two independent detections happen to fall inside the coincidence timing window, even though they do not originate from the same annihilation. In PET this typically means that two unrelated 511 keV photons, often from different decays, are detected close enough in time that the digitizer classifies them as a coincidence pair. For image formation, randoms are undesirable because they add a nearly uniform background and degrade image contrast while increasing noise.
In a real scanner you cannot directly label an event as random or not, but in a Monte Carlo simulation with GATE you have access to extra truth information that allows you to classify coincidences. Understanding and using this information correctly is essential if you want to study random fractions, optimize acquisition parameters, or validate randoms correction methods.
In GATE based PET simulations, each detected single usually carries identifiers such as an event ID and sometimes a parent or source ID that indicate which primary particle or annihilation the detection originated from. When a coincidence sorter in the digitizer pairs two singles, it typically records, for each member of the pair, at least the detector positions, deposited energies, detection times, and these event or source identifiers. After the simulation finishes, you analyze the coincidence list and compare the identifiers of the two singles forming each coincidence.
For most PET configurations, you classify a coincidence as random when the two singles belong to different annihilation events. In practice, this usually means that the event IDs of the two members of a coincidence are different. If you have more detailed information, such as a specific annihilation ID or parent gamma ID, you can use that instead, but for a basic beginner analysis the event ID comparison is sufficient.
You can summarize the simple classification rule as:
A coincidence is a random if the two singles in the pair do not share the same origin, for example if their event IDs are different.
In contrast, coincidences where both singles share the same annihilation are true coincidences, and those where at least one of the photons has scattered in the patient or detector before detection are scattered coincidences, as discussed in other sections of this chapter. When you write your analysis code, you typically loop over all coincidence entries in the output file. For each coincidence you read the identifiers of the first and second single, test whether they are equal or different, and increment counters for true, scatter, and random categories accordingly.
Once you have separated random coincidences, you can compute performance metrics such as the random fraction or random rate, often as a function of activity or coincidence timing window. The random coincidence rate $R$ for a given acquisition can be estimated directly from the classified list by counting how many coincidences are labeled as random and dividing by the acquisition time. Ratios like $R/(T+S+R)$, where $T$ is the number of true coincidences and $S$ the number of scattered coincidences, help you quantify how strongly randoms affect image quality for a given scanner and acquisition protocol.
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