# A lifted Bregman strategy for training unfolded proximal neural network Gaussian denoisers

arXiv: https://arxiv.org/abs/2408.08742 · HTML: https://mlsanity.com/paper/2408.08742/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 38 references that are in the map.
- First posted on arXiv 16 Aug 2024.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Training Neural Networks Without Gradients: A Scalable ADMM Approach](https://mlsanity.com/paper/1605.02026/) (2016)
- [Deep Neural Network Structures Solving Variational Inequalities](https://mlsanity.com/paper/1808.07526/) (2018)
- [Fenchel Lifted Networks: A Lagrange Relaxation of Neural Network Training](https://mlsanity.com/paper/1811.08039/) (2018)
- [Lifted Bregman Training of Neural Networks](https://mlsanity.com/paper/2208.08772/) (2022)
- [Contrastive Learning for Lifted Networks](https://mlsanity.com/paper/1905.02507/) (2019)
- [A deep primal-dual proximal network for image restoration](https://mlsanity.com/paper/2007.00959/) (2020)
- [A Lifted Bregman Formulation for the Inversion of Deep Neural Networks](https://mlsanity.com/paper/2303.01965/) (2023)
- [An alternative approach to train neural networks using monotone variational inequality](https://mlsanity.com/paper/2202.08876/) (2022)
- [A Variational Inequality Model for Learning Neural Networks](https://mlsanity.com/paper/2210.15064/) (2022)

## Abstract (arXiv)

Unfolded proximal neural networks (PNNs) form a family of methods that combines deep learning and proximal optimization approaches. They consist in designing a neural network for a specific task by unrolling a proximal algorithm for a fixed number of iterations, where linearities can be learned from prior training procedure. PNNs have shown to be more robust than traditional deep learning approaches while reaching at least as good performances, in particular in computational imaging. However, training PNNs still depends on the efficiency of available training algorithms. In this work, we propose a lifted training formulation based on Bregman distances for unfolded PNNs. Leveraging the deterministic mini-batch block-coordinate forward-backward method, we design a bespoke computational strategy beyond traditional back-propagation methods for solving the resulting learning problem efficiently. We assess the behaviour of the proposed training approach for PNNs through numerical simulations on image denoising, considering a denoising PNN whose structure is based on dual proximal-gradient iterations.