# A deep primal-dual proximal network for image restoration

arXiv: https://arxiv.org/abs/2007.00959 · HTML: https://mlsanity.com/paper/2007.00959/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2020.

## Built on by (most cited first, 9 of 9)

- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [WPPNets and WPPFlows: The Power of Wasserstein Patch Priors for Superresolution](https://mlsanity.com/paper/2201.08157/) (2022)
- [Unfolded proximal neural networks for robust image Gaussian denoising](https://mlsanity.com/paper/2308.03139/) (2023)
- [Stochastic Unrolled Federated Learning](https://mlsanity.com/paper/2305.15371/) (2023)
- [Restarted contractive operators to learn at equilibrium](https://mlsanity.com/paper/2506.13239/) (2025)
- [Alternative design of DeepPDNet in the context of image restoration](https://mlsanity.com/paper/2202.09810/) (2022)
- [A lifted Bregman strategy for training unfolded proximal neural network Gaussian denoisers](https://mlsanity.com/paper/2408.08742/) (2024)
- [Analysis and Synthesis Denoisers for Forward-Backward Plug-and-Play Algorithms](https://mlsanity.com/paper/2411.13276/) (2024)
- [Restore What Matters: Lessons from Joint Restoration and Recognition](https://mlsanity.com/paper/2609.13791/) (2026)

## Abstract (arXiv)

Image restoration remains a challenging task in image processing. Numerous methods tackle this problem, often solved by minimizing a non-smooth penalized co-log-likelihood function. Although the solution is easily interpretable with theoretic guarantees, its estimation relies on an optimization process that can take time. Considering the research effort in deep learning for image classification and segmentation, this class of methods offers a serious alternative to perform image restoration but stays challenging to solve inverse problems. In this work, we design a deep network, named DeepPDNet, built from primal-dual proximal iterations associated with the minimization of a standard penalized likelihood with an analysis prior, allowing us to take advantage of both worlds. We reformulate a specific instance of the Condat-Vu primal-dual hybrid gradient (PDHG) algorithm as a deep network with fixed layers. The learned parameters are both the PDHG algorithm step-sizes and the analysis linear operator involved in the penalization (including the regularization parameter). These parameters are allowed to vary from a layer to another one. Two different learning strategies: "Full learning" and "Partial learning" are proposed, the first one is the most efficient numerically while the second one relies on standard constraints ensuring convergence in the standard PDHG iterations. Moreover, global and local sparse analysis prior are studied to seek a better feature representation. We apply the proposed methods to image restoration on the MNIST and BSD68 datasets and to single image super-resolution on the BSD100 and SET14 datasets. Extensive results show that the proposed DeepPDNet demonstrates excellent performance on the MNIST and the more complex BSD68, BSD100, and SET14 datasets for image restoration and single image super-resolution task.