  We present a novel approach to image restoration that leverages ideas from
localized structured prediction and non-linear multi-task learning. We optimize
a penalized energy function regularized by a sum of terms measuring the
distance between patches to be restored and clean patches from an external
database gathered beforehand. The resulting estimator comes with strong
statistical guarantees leveraging local dependency properties of overlapping
patches. We derive the corresponding algorithms for energies based on the
mean-squared and Euclidean norm errors. Finally, we demonstrate the practical
effectiveness of our model on different image restoration problems using
standard benchmarks.
