The present work deals with the development of a novel approach to increase the quality of 3D vector-valued (4D) images. We model the problem as a coupled anisotropic convection diffusion filtering scheme based upon local structure analysis. The orientation of the denoising and shock filtering are based upon an analysis of the local structure of the vector-valued image through a tensor that accounts for the distribution of the noise between the channels. With this approach, the noise is reduced in homogeneous regions while the vector edges are sharpened orthogonally to the flow of diffusion. We present the continuous problem and a corresponding discretization in space and time by a numerical way. Results on realistic dynamic PET image simulations illustrate the potential of the proposed method, which led to distinct improvements of figures of merit over several other approaches from the literature.