We propose a convex variational framework to compute high resolution images from a low resolution video. The image formation process is analyzed to provide to a well designed model for warping, blurring, downsampling and regularization. We provide a comprehensive investigation of the single model components. The super-resolution problem is modeled as a minimization problem in an unified convex framework, which is solved by a fast primal dual algorithm. A comprehensive evaluation on the influence of different kinds of noise is carried out. The proposed algorithm shows excellent recovery of information for various real and synthetic datasets.