We propose a nonparametric and Bayesian method for reconstructing dynamic Positron Emission Tomography (PET) images from clinical data. PET is a nuclear medicine imaging modality that uses molecules labeled with a positron emitting radionuclide. It is then possible to image in vivo molecular interactions of biological processes. Our approach is non-parametric in the sense that the image representing the 4D (3D+t) activity distribution is viewed as a probability density on R 3 × R + and inferred directly from the data, without any prior space or time discretization. Being nonparametric, we do not pre-assume any particular functional form for this space-time distribution. Formulating the nonparametric problem in the Bayesian framework allows to characterize the entire 4D distribution of the unknown. Furthermore, this framework allows to access directly to the reconstruction error. The ability of the proposed model is assessed using data from clinical studies and we evaluate its performance against the conventional independent time-frame reconstruction approach using the maximum likelihood algorithm (ML-EM).