  This paper proposes a novel approach to image 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
image 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 deblurring 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 learning problem is not convex, once the dictionaries have been learned,
the sharp/high-resolution image can be recovered via convex optimization at
test time. Experiments with synthetic and real data demonstrate the
effectiveness of the proposed approach, leading to state-of-the-art performance
for non-blind image deblurring and digital zoom.
