  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.
