# Bregman Plug-and-Play Priors

arXiv: https://arxiv.org/abs/2202.02388 · HTML: https://mlsanity.com/paper/2202.02388/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 32 references that are in the map.
- First posted on arXiv 4 Feb 2022.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Relatively-Smooth Convex Optimization by First-Order Methods, and Applications](https://mlsanity.com/paper/1610.05708/) (2016)
- [Regularization by Denoising: Clarifications and New Interpretations](https://mlsanity.com/paper/1806.02296/) (2018)
- [Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds](https://mlsanity.com/paper/1808.10038/) (2018)
- [Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolation](https://mlsanity.com/paper/1512.07331/) (2015)
- [An Online Plug-and-Play Algorithm for Regularized Image Reconstruction](https://mlsanity.com/paper/1809.04693/) (2018)
- [RARE: Image Reconstruction using Deep Priors Learned without Ground Truth](https://mlsanity.com/paper/1912.05854/) (2019)
- [Scalable Plug-and-Play ADMM with Convergence Guarantees](https://mlsanity.com/paper/2006.03224/) (2020)
- [Provable Convergence of Plug-and-Play Priors with MMSE denoisers](https://mlsanity.com/paper/2005.07685/) (2020)
- [Poisson Inverse Problems by the Plug-and-Play scheme](https://mlsanity.com/paper/1511.02500/) (2015)
- [Boosting the Performance of Plug-and-Play Priors via Denoiser Scaling](https://mlsanity.com/paper/2002.11546/) (2020)

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

- [Convergent Bregman Plug-and-Play Image Restoration for Poisson Inverse Problems](https://mlsanity.com/paper/2306.03466/) (2023)
- [Deep Equilibrium models for Poisson Imaging Inverse problems via Mirror Descent](https://mlsanity.com/paper/2507.11461/) (2025)
- [Learning truly monotone operators with applications to nonlinear inverse problems](https://mlsanity.com/paper/2404.00390/) (2024)

## Abstract (arXiv)

The past few years have seen a surge of activity around integration of deep learning networks and optimization algorithms for solving inverse problems. Recent work on plug-and-play priors (PnP), regularization by denoising (RED), and deep unfolding has shown the state-of-the-art performance of such integration in a variety of applications. However, the current paradigm for designing such algorithms is inherently Euclidean, due to the usage of the quadratic norm within the projection and proximal operators. We propose to broaden this perspective by considering a non-Euclidean setting based on the more general Bregman distance. Our new Bregman Proximal Gradient Method variant of PnP (PnP-BPGM) and Bregman Steepest Descent variant of RED (RED-BSD) replace the traditional updates in PnP and RED from the quadratic norms to more general Bregman distance. We present a theoretical convergence result for PnP-BPGM and demonstrate the effectiveness of our algorithms on Poisson linear inverse problems.