Noise suppression is particularly important in low count positron emission tomography (PET) imaging. Post-smoothing (PS) and regularization methods which aim to reduce noise also tend to reduce resolution and introduce bias. Alternatively, anatomical information from another modality such as magnetic resonance (MR) imaging can be used to improve image quality. Convolutional neural networks (CNNs) are particularly well suited to such joint image processing, but usually require large amounts of training data and have mostly been applied outside the field of medical imaging or focus on classification and segmentation, leaving PET image quality improvement relatively understudied. This project proposes the use of a relatively low-complexity CNN (micro-net) as a post-reconstruction MR-guided image processing step to reduce noise and reconstruction artefacts while also improving resolution in low count PET scans. The CNN is designed to be fully 3-D, robust to very limited amounts of training data, and to accept multiple inputs (including competitive denoising methods).