Diffusion Tensor Imaging (DTI) provides us with valuable information about the white matter fibers and their arrangement in the brain. However, clinical DTI acquisitions are often low resolution, causing partial volume effects. In this paper, we propose a new high resolution tensor estimation method. This method makes use of the spatial correlation between neighboring voxels. Unlike some super-resolution algorithms, the proposed method does not require multiple acquisitions, thus it is better suited for clinical situations. The method relies on a maximum likelihood strategy for tensor estimation to optimally account for the noise and an anisotropic regularization prior to promote smoothness in homogeneous areas while respecting the edges. To the best of our knowledge, this is the first method to produce high resolution tensor images from a single low resolution acquisition. We demonstrate the efficiency of the method on synthetic low-resolution data and real clinical data. The results show statistically significant improvements in fiber tractography.