# Revisiting loss-specific training of filter-based MRFs for image restoration

arXiv: https://arxiv.org/abs/1401.4107 · HTML: https://mlsanity.com/paper/1401.4107/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2014.

## Built on by (most cited first, 3 of 3)

- [On Optimal Regularization Parameters via Bilevel Learning](https://mlsanity.com/paper/2305.18394/) (2023)
- [Fixed-Point Automatic Differentiation of Forward--Backward Splitting Algorithms for Partly Smooth Functions](https://mlsanity.com/paper/2208.03107/) (2022)
- [Can We Use Neural Regularization to Solve Depth Super-Resolution?](https://mlsanity.com/paper/2112.11085/) (2021)

## Abstract (arXiv)

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.