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A novel digital signal processing method called digital-single-event-reconstruction (DiSER) is proposed to detect pileups, and to recover the timing and the energy information of each single event from a pileup. For each digitized waveform, the DiSER method can distinguish multi-event pileups from single-event pulses by counting the leading edges in a scintillation's duration. Leading edges are identified from the derivative of the waveform. Each leading edge and its following tail are utilized to reconstruct the scintillation pulses in a pileup. Two or more reconstructed single-event pulses can be retrieved from a detected pileup. Consequently, the timing and the energy information of the single event could be derived from the reconstructed pulse. Compared to the conventional pulse processing method, the DiSER method significantly increases the counts of coincidence events in high count rate cases. The energy spectrums, coincidence timing histograms and flood maps obtained by the DiSER method and the conventional method are compared. The effect of sampling rate on the DiSER performance is investigated as well. The experimental results suggest that the DiSER method is a promising digitally sampling scintillation pulses technique for pileup processing in PET.