With continuing improvements in spatial resolution of positron emission tomography (PET) scanners, small patient movements during PET imaging become a significant source of resolution degradation. This work develops and investigates a comprehensive formalism for accurate motion-compensated reconstruction which at the same time is very feasible in the context of high-resolution PET. In particular, this paper proposes an effective method to incorporate presence of scattered and random coincidences in the context of motion (which is similarly applicable to various other motion correction schemes). The overall reconstruction framework takes into consideration missing projection data which are not detected due to motion, and additionally, incorporates information from all detected events, including those which fall outside the field-of-view following motion correction. The proposed approach has been extensively validated using phantom experiments as well as realistic simulations of a new mathematical brain phantom developed in this work, and the results for a dynamic patient study are also presented.