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In this study, we implemented a fully 3D maximum likelihood ordered subsets expectation maximization (ML-OSEM) reconstruction algorithm with two methods for corrections of randoms, and scatter coincidences: (a) measured data were pre-corrected for randoms and scatter, and (b) corrections were incorporated into the iterative algorithm. In 3D PET acquisitions, the random and scatter coincidences constitute a significant fraction of the measured coincidences. ML-OSEM reconstruction algorithms make assumptions of Poisson distributed data. Pre-corrections for random and scatter coincidences result in deviations from that assumption, potentially leading to increased noise and inconsistent convergence. Incorporating the corrections inside the loop of the iterative reconstruction preserves the Poisson nature of the data. We performed Monte Carlo simulations with different randoms fractions and reconstructed the data with the two methods. We also reconstructed clinical patient images. The two methods were compared quantitatively through contrast and noise measurements. The results indicate that for high levels of randoms, incorporating the corrections inside the iterative loop results in superior image quality.