The effect of count statistics on the convergence value in OSEM reconstruction in PET and TOF PET

Ordered Subsets Expectation Maximization (OSEM) has been introduced to greatly reduce reconstruction time compared to Maximum Likelihood Expectation Maximization (MLEM) in Positron Emission Tomography (PET). In case of noise-free data, OSEM converges to a MLEM image, but in presence of noise this might not be true, and also OSEM might not converge at all but cycle between similar but distinct images. Assessing what are the limits of the OSEM in terms of reliable contrast recovery is particularly interesting in situation of very short acquisitions and very sparse data. In this work, we study the convergence value of the contrast recovery as a function of the count statistics (and therefore the noise level) in the PET data, using a NEMA image quality phantom. A comparison between Time-of-Flight (TOF) and non-TOF implementations is performed. The scope of the work is to assess how the count statistics affects the convergence value and the convergence rate for OSEM reconstruction, and then to compare the corresponding convergence rates in conventional PET and in TOF PET reconstructions, by analyzing both experimental and simulated data.