Impact of Time Of Flight on early-stopped Maximum-Likelihood Expectation Maximization PET reconstruction

The use of Time Of Flight (TOF) in Positron Emission Tomography (PET) is expected to reduce noise on images, thanks to the additional information. In clinical routine, a common reconstruction approach is the use of maximum likelihood expectation maximization (MLEM) stopped after few iterations. Empirically it was reported that, at matched number of iterations, the introduction of TOF increases noise. In this work we revise the theory describing the signal and noise convergence in MLEM, and we adapt it to describe the TOF impact on early stopped MLEM. We validated theoretical results using both computer simulations and phantom measurements, performed on scanners with different coincidence timing resolutions. This work provides theoretical support for the empirically observed noise increase introduced by TOF. Conversely, it shows that TOF not only improves signal convergence but also makes it less dependent on the activity distribution in the field of view. We then propose a strategy to determine stopping criteria for TOF-MLEM, which reduces the number of iterations by a factor proportional to the coincidence timing resolution. We prove that this criteria succeeds in markedly reducing noise, while improving signal recovery robustness as it provides a level of contrast recovery which is independent from the object dimension and from the activity distribution of the background.