I. Introduction
In positron emission tomography (PET) studies, the measurement of the arrival time difference of coincident gamma-ray pairs (time-of-flight (TOF) information) allows more accurate localization of positron emitters on the line-of-response (LOR), leading to improved reconstructed PET image quality [1]–[3]. Propagation of image noise along the LOR during the projection process in image reconstruction is limited within a restricted space (segmented LOR) using the TOF information, enhancing the signal-to-noise ratio (SNR) of PET images [4]. Accordingly, the TOF measurement improves the diagnostic power of PET and/or reduces the scan time or radiation dose [5], [6]. Another benefit of TOF information is the mitigation of image artifacts due to inconsistent or missing data in PET measurements [7], [8]. In addition, the joint estimation of activity and attenuation data can be facilitated by the improved TOF measurement, and is useful in reducing artifacts due to the misalignment of emission and transmission data and ultimately eliminating the necessity of transmission data for PET attenuation correction [9], [10].