Diffusion tensor imaging (DTI) is currently being refined as a tool to study the course of nerve fibre bundles in the human brain. Using DTI, the local fibre orientation in each image voxel can be described by a diffusion tensor which is constructed from local measurements of diffusion coefficients along several directions. The measured diffusion coefficients and thereby the diffusion tensors are subject to noise, leading to possibly flawed representations of the three dimensional fibre bundles. Efforts to reduce noise by regularization have so far been concentrated on the analysis of the primary diffusion direction. In this paper we develop a Bayesian procedure for regularizing the full diffusion tensor field, fully utilizing the available three-dimensional information of fibre orientation. The use of the procedure is exemplified on synthetic and in vivo data.