In this paper we propose a novel algorithm for jointly performing data based motion correction and direct parametric reconstruction of dynamic PET data. We derive a closed form update for the penalised likelihood maximisation which greatly enhances the algorithm's computational efficiency for practical use. Our algorithm achieves sub-voxel motion correction residual with noisy data in the simulation-based validation and reduces the bias of the direct estimation of the kinetic parameter of interest. A preliminary evaluation on clinical brain data using [18F]Choline shows improved contrast for regions of high activity. The proposed method is based on a data-driven kinetic modelling method and is directly applicable to reversible and irreversible PET tracers, covering a range of clinical applications.