Deep image prior (DIP) has recently attracted attention owing to its unsupervised positron emission tomography (PET) image reconstruction, which does not require any prior training dataset. In this paper, we present the first attempt to implement an end-to-end DIP-based fully 3D PET image reconstruction method that incorporates a forward-projection model into a loss function. To implement a practical fully 3D PET image reconstruction, which could not be performed due to a graphics processing unit memory limitation, we modify the DIP optimization to block-iteration and sequentially learn an ordered sequence of block sinograms. Furthermore, the relative difference penalty (RDP) term was added to the loss function to enhance the quantitative PET image accuracy. We evaluated our proposed method using Monte Carlo simulation with [$^{18}$F]FDG PET data of a human brain and a preclinical study on monkey brain [$^{18}$F]FDG PET data. The proposed method was compared with the maximum-likelihood expectation maximization (EM), maximum-a-posterior EM with RDP, and hybrid DIP-based PET reconstruction methods. The simulation results showed that the proposed method improved the PET image quality by reducing statistical noise and preserved a contrast of brain structures and inserted tumor compared with other algorithms. In the preclinical experiment, finer structures and better contrast recovery were obtained by the proposed method. This indicated that the proposed method can produce high-quality images without a prior training dataset. Thus, the proposed method is a key enabling technology for the straightforward and practical implementation of end-to-end DIP-based fully 3D PET image reconstruction.

List-mode positron emission tomography (PET) image reconstruction is an important tool for PET scanners with many lines-of-response and additional information such as time-of-flight and depth-of-interaction. Deep learning is one possible solution to enhance the quality of PET image reconstruction. However, the application of deep learning techniques to list-mode PET image reconstruction has not been progressed because list data is a sequence of bit codes and unsuitable for processing by convolutional neural networks (CNN). In this study, we propose a novel list-mode PET image reconstruction method using an unsupervised CNN called deep image prior (DIP) which is the first trial to integrate list-mode PET image reconstruction and CNN. The proposed list-mode DIP reconstruction (LM-DIPRecon) method alternatively iterates the regularized list-mode dynamic row action maximum likelihood algorithm (LM-DRAMA) and magnetic resonance imaging conditioned DIP (MR-DIP) using an alternating direction method of multipliers. We evaluated LM-DIPRecon using both simulation and clinical data, and it achieved sharper images and better tradeoff curves between contrast and noise than the LM-DRAMA, MR-DIP and sinogram-based DIPRecon methods. These results indicated that the LM-DIPRecon is useful for quantitative PET imaging with limited events while keeping accurate raw data information. In addition, as list data has finer temporal information than dynamic sinograms, list-mode deep image prior reconstruction is expected to be useful for 4D PET imaging and motion correction.