International Journal of Computer Vision manuscript No. (will be inserted by the editor) Dictionary Learning for Deblurring and Digital Zoom

Abstract This paper proposes a novel approach to im-age deblurring and digital zooming using sparse local models of image appearance. These models, where small image patches are represented as linear combinations of a few elements drawn from some large set (dictionary) of candidates, have proven well adapted to several im-age restoration tasks. A key to their success has been to learn dictionaries adapted to the reconstruction of small image patches. In contrast, recent works have proposed instead to learn dictionaries which are not only adapted to data reconstruction, but also tuned for a specific task. We introduce here such an approach to deblur-ring and digital zoom, using pairs of blurry/sharp (or low-/high-resolution) images for training, as well as an effective stochastic gradient algorithm for solving the corresponding optimization task. Although this learn-ing problem is not convex, once the dictionaries have been learned, the sharp/high-resolution image can be F. Couzinie-Devy Willow Project-Team, Laboratoire d’Informatique de l’Écol