  It is now well known that Markov random fields (MRFs) are particularly
effective for modeling image priors in low-level vision. Recent years have seen
the emergence of two main approaches for learning the parameters in MRFs: (1)
probabilistic learning using sampling-based algorithms and (2) loss-specific
training based on MAP estimate. After investigating existing training
approaches, it turns out that the performance of the loss-specific training has
been significantly underestimated in existing work. In this paper, we revisit
this approach and use techniques from bi-level optimization to solve it. We
show that we can get a substantial gain in the final performance by solving the
lower-level problem in the bi-level framework with high accuracy using our
newly proposed algorithm. As a result, our trained model is on par with highly
specialized image denoising algorithms and clearly outperforms
probabilistically trained MRF models. Our findings suggest that for the
loss-specific training scheme, solving the lower-level problem with higher
accuracy is beneficial. Our trained model comes along with the additional
advantage, that inference is extremely efficient. Our GPU-based implementation
takes less than 1s to produce state-of-the-art performance.
