Object size dependency of noise strength and correlation patterns for TOF and non-TOF PET

We investigate noise strength and correlation length tradeoffs for non time-of-flight (TOF) and TOF penalized likelihood image reconstruction as functions of object size and imaging system timing resolution. We show that for non-TOF imaging, noise correlation lengths have a strong dependence on object size. When smoothing parameters are varied to match correlation lengths among different sized objects, noise levels differ greatly. Since TOF-PET is a better conditioned reconstruction problem compared to the non-TOF case and mostly benefits larger objects, we investigate whether TOF is able to reduce the object size dependency of noise strength and correlation lengths. Through analytic expressions and Monte Carlo simulations, we show that as the timing resolution improves, noise correlation lengths in larger objects are shortened and it becomes possible to reduce their dependence on object size. Noise texture across the body is therefore more uniform with TOF-PET whole body imaging compared to non-TOF imaging.