Cardiac Positron Emission Tomography (PET) can provide diagnostic information about myocardial perfusion and metabolism with excellent sensitivity. The main challenge is physiological motion of the heart due to breathing and heartbeat. Here we present a joint PET-MR image registration approach which provides non-rigid cardiac and respiratory motion information utilising image data from a simultaneous PET-MR scan of less than 4min. In addition, attenuation correction information is also derived from the MR scan. The motion information is utilised in a motion-corrected PET image reconstruction which improves PET image quality, enhances visualisation of small features and increases measured uptake values by 22±7%.