Positron emission tomography (PET) is a widely used molecular imaging modality,which offers quantitative information about many biochemical processes in vivo.In particular, the dynamic PET data provide physiologically meaningful parametricimages after the estimation of the parameters of a model that best describes thekinetic behaviour of the injected radiotracer. Spatiotemporal 4D image reconstructionalgorithms estimate these physiological parameters directly from the raw sinogramdata, where the noise distribution can be more accurately modelled and thus leading tostatistically more reliable parameter estimates. In this thesis a novel direct parametricimage reconstruction algorithm is introduced, which is based on the expectationmaximisation (EM) framework and is applicable to any spatiotemporal model. Themethod is evaluated for the spectral analysis model, which is a linear temporal modeland a two-tissue compartment model, which is a nonlinear temporal model. Inaddition, the method is evaluated for a linear spatial model and in particular the modelthat is normally used to describe the blurring components in image-based resolutionmodelling. Finally, the performance of gradient-based 3D reconstruction algorithmswas also assessed as an alternative to the well-established EM-based algorithms.