Theoretical investigation of the effects of timing calibration errors on time-of-flight PET image quality

Miscalibration of Time-of-Flight (TOF) PET systems can result in significant degradation in reconstructed image quality. We present two expressions for pixel-wise image covariance estimation in the presence of mismatch between the acquisition and reconstruction system models.We applied these two approaches to investigate the effect of calibration errors in the timing delay across detectors. We simulated a 200ps coincidence timing resolution TOF-PET system with nominally no timing delays across detectors. We simulated four uncalibrated systems where the timing delay across detectors were Gaussian distributed with zero mean and standard deviations of 50, 100, 200, and 300 ps. We generated sinograms for a 45cm x 30cm elliptical phantom with two lesions using forward projectors that modeled the 4 uncalibrated systems. The two methods resulted in similar estimates of image noise when the calibration errors were small but produced very different estimates for large calibration errors. To verify the accuracy of the two approaches we estimated the image variance using Monte Carlo simulations for the systems with 50 and 300 ps timing delay calibration error. The second approximation, which is based on expanding the Taylor series around the actual data mean, showed good agreement with Monte-Carlo simulations and was found to be more accurate for large calibration errors.