The Maximum Likelihood-Expectation Maximization (ML-EM) algorithm is the most popular statistical reconstruction technique for Positron Emission Tomography (PET). The ML-EM algorithm is however also renowned for its long reconstruction times. An acceleration technique for this algorithm is studied in this paper. The proposed technique starts the ML-EM algorithm before the measurement process is completed. Since the reconstruction is initiated during the scan of the patient, the time elapsed before a reconstruction becomes available is reduced. Experiments with software phantoms indicate that the quality of the reconstructed image using successive data is comparable to the quality of the reconstruction with the normal ML-EM algorithm. (authors). 7 refs, 3 figs.