  We propose a deep reparametrization of the maximum a posteriori formulation
commonly employed in multi-frame image restoration tasks. Our approach is
derived by introducing a learned error metric and a latent representation of
the target image, which transforms the MAP objective to a deep feature space.
The deep reparametrization allows us to directly model the image formation
process in the latent space, and to integrate learned image priors into the
prediction. Our approach thereby leverages the advantages of deep learning,
while also benefiting from the principled multi-frame fusion provided by the
classical MAP formulation. We validate our approach through comprehensive
experiments on burst denoising and burst super-resolution datasets. Our
approach sets a new state-of-the-art for both tasks, demonstrating the
generality and effectiveness of the proposed formulation.
