TOF Modeling with a Double Gaussian Function

Positron emission tomography (PET) applies the time information in the image reconstruction to enhance the image quality. However, conventional time-of-flight (TOF) modeling with a single Gaussian function cannot meet the requirements of various detector designs. For instance, if the detectors involve single events with Cherenkov radiation or Compton scatter recovery (CSR), a multiple Gaussian function is more suitable rather than a single Gaussian function. In this abstract, the double Gaussian function with two different sets of configurations is applied to conduct time blurring on the single events of simulated coincidences, and the projection data are analyzed regarding the TOF resolution and image quality (IQ) phantom, as described in NEMA 2018 standard. In theory, we prove that the double Gaussian model for the singles results in a tri-Gaussian model for the coincidences. If one part of double Gaussian function is dominant for singles, the tri-Gaussian model can be simplified as a double Gaussian model. This point is further convinced by the TOF resolution simulations, where the fitting of a double Gaussian function is relatively accurate enough. The results of the IQ phantom simulations demonstrate that the double Gaussian model has no significant differences compared to the single Gaussian model regarding the six spheres. However, in terms of the lung residual error, the double Gaussian model outperforms the single Gaussian model, indicating the importance of a matched TOF model. The improvement is observed to be more significant when the mismatch between the single Gaussian function and time error profiles get larger.