This paper presents a generative model for super-resolution in routine clinical magnetic resonance images (MRI), of arbitrary orientation and contrast. The model recasts the recovery of high resolution images as an inverse problem, in which a forward model simulates the slice-select profile of the MR scanner. The paper introduces a prior based on multi-channel total variation for MRI super-resolution. Bias-variance trade-off is handled by estimating hyper-parameters from the low resolution input scans. The model was validated on a large database of brain images. The validation showed that the model can improve brain segmentation, that it can recover anatomical information between images of different MR contrasts, and that it generalises well to the large variability present in MR images of different subjects