<title>Abstract</title>
Objective. Convolutional neural networks (CNNs) are a strong tool for improving the coincidence time resolution of time-of-flight (TOF) positron emission tomography detectors. However, several signal waveforms from multiple source positions are required for CNN training. Furthermore, there is concern that TOF estimation is biased near the edge of the training space, despite the reduced estimation variance (i.e., timing uncertainty). Approach. We propose a simple method for unbiased TOF estimation by combining a conventional leading-edge discriminator (LED) and a CNN that can be trained with waveforms collected from one source position. The proposed method estimates and corrects the time difference error calculated by the LED rather than the absolute time difference. This model can eliminate the TOF estimation bias, as the combination with the LED converts the distribution of the label data from discrete values at each position into a continuous symmetric distribution. Main results. Evaluation results using signal waveforms collected from scintillation detectors show that the proposed method can correctly estimate all source positions without bias from a single source position. Moreover, the proposed method improves the coincidence time resolution of the conventional LED. Significance. We believe that the improved CTR will not only increase the signal-to-noise ratio but will also contribute significantly to a part of the direct positron emission imaging.