Rethinking Timing Residuals: Advancing PET Detectors with Explicit TOF Corrections

PET is a functional imaging method that visualizes metabolic processes. TOF information can be derived from coincident detector signals and incorporated into image reconstruction to enhance the SNR. PET detectors are typically assessed by their CTR, but timing performance is degraded by various factors. Research on timing calibration seeks to mitigate these degradations and restore accurate timing information. While many calibration methods use analytical approaches, machine learning techniques have recently gained attention due to their flexibility. We developed a residual physics-based calibration approach that combines prior domain knowledge with the power of machine learning models. This approach begins with an initial analytical calibration addressing first-order skews. The remaining deviations, regarded as residual effects, are used to train machine learning models to eliminate higher-order skews. The key advantage is that the experimenter guides the learning process through the definition of timing residuals. In earlier studies, we developed models that directly predicted the expected time difference, which offered corrections only implicitly (implicit correction models). In this study, we introduce a new definition for timing residuals, enabling us to train models that directly predict correction values (explicit correction models). The explicit correction approach significantly simplifies data acquisition, improves linearity, and enhances timing performance from $371 \pm 6$ ps to $281 \pm 5$ ps for coincidences from 430 keV to 590 keV. Additionally, the new definition reduces model size, making it suitable for high-throughput applications like PET scanners. Experiments were conducted using two detector stacks composed of $4 \times 4$ LYSO:Ce,Ca crystals ($3.8\times 3.8\times 20$ mm$^{3}$) coupled to $4 \times 4$ Broadcom NUV-MT SiPMs and digitized with the TOFPET2 ASIC.