Total-body positron emission tomography (PET) scanners are proposed as a solution to the inferior sensitivity and long scan times of regular PET systems. The increased axial field-of-view (FOV) however requires a vast amount of scintillation material and electronics making them too expensive for widespread clinical use. Monolithic detectors are attractive for total-body PET because of their cost-effectiveness while maintaining high spatial resolution and providing depth-of-interaction (DOI) information. Introduction of detector gaps in the scanner design can further reduce system costs significantly. These alterations make total-body PET more affordable but require advanced signal processing algorithms in order to maintain favorable image quality, for which we propose the use of deep learning. This research focuses on improving three aspects of the imaging process: 1. gamma photon arrival time estimation in monolithic detectors to improve time-of-flight (TOF) resolution, 2. identification of Compton scattering in monolithic crystals to improve positioning of gamma interactions and 3. image recovery for total-body PET systems featuring a large amount of detector gaps. Data required for training and evaluating the neural networks will be acquired by GATE Monte Carlo simulation, enriched by experiments where possible. Although this research focuses on total-body PET, many of its results will also be applicable to and improve performance of regular PET systems.