I. Introduction
Recently there has been a growing interest in the time-of-flight (TOF) positron emission tomography (PET) scanner, because the incorporation of the TOF technique into PET (current time resolution of ) has demonstrated a significant improvement in image quality [1], [2]. The TOF information, which is the difference in the arrival times of the two annihilation gamma-rays, provides localization of the annihilation position on the line-of-response (LOR) [3]–[5]. This allows the use of a segment-of-response (SOR) instead of LOR in image reconstruction, and reduces the propagation of noise along the LOR in the reconstructed images. The reduction of noise can be equated with an increase in sensitivity [6]. Furthermore, the additional TOF information enables PET images to achieve high signal-to-noise ratio (SNR) and high contrast, or short scan times [1], [4], [7].