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Pileup correction in PET imaging is a complex problem to tackle. In most cases pileup is rejected which increases the detector deadtime. This paper describes a method to train a Convolutional Neural Network to separate the pileup peaks and provide their relative arrival times. ADC raw signal events are collected to establish a collection of non-pileup events. These events were then summed to generate no pileup, 2, and 3 events pileup conditions. A Convolution Neural Network (CNN) is constructed and trained to accept these synthetic pileup events and their corresponding constituent events. Data of pileup events with accurate timemarks was collected and the same CNN was used to separate the pileup events. Then the CNN was modified to add the timemark difference between the pileup events as an output, and the network was retrained with the collected pileup data set and their time difference. The result is a detector raw signal input to the trained network, and the output is the same event if there is no pileup or separated events with their time differences if there is pileup.