# Convergent Bregman Plug-and-Play Image Restoration for Poisson Inverse Problems

arXiv: https://arxiv.org/abs/2306.03466 · HTML: https://mlsanity.com/paper/2306.03466/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 43 references that are in the map.
- First posted on arXiv 6 Jun 2023.

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

- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Noise2Score: Tweedie's Approach to Self-Supervised Image Denoising without Clean Images](https://mlsanity.com/paper/2106.07009/) (2021)
- [Gradient Step Denoiser for convergent Plug-and-Play](https://mlsanity.com/paper/2110.03220/) (2021)
- [Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularization](https://mlsanity.com/paper/2201.13256/) (2022)
- [Scalable Plug-and-Play ADMM with Convergence Guarantees](https://mlsanity.com/paper/2006.03224/) (2020)
- [First Order Methods beyond Convexity and Lipschitz Gradient Continuity with Applications to Quadratic Inverse Problems](https://mlsanity.com/paper/1706.06461/) (2017)
- [A characterization of proximity operators](https://mlsanity.com/paper/1807.04014/) (2018)
- [iPiano: Inertial Proximal Algorithm for Non-Convex Optimization](https://mlsanity.com/paper/1404.4805/) (2014)
- [Poisson Inverse Problems by the Plug-and-Play scheme](https://mlsanity.com/paper/1511.02500/) (2015)
- [A relaxed proximal gradient descent algorithm for convergent plug-and-play with proximal denoiser](https://mlsanity.com/paper/2301.13731/) (2023)
- [Photon Limited Non-Blind Deblurring Using Algorithm Unrolling](https://mlsanity.com/paper/2110.15314/) (2021)
- [Bregman Plug-and-Play Priors](https://mlsanity.com/paper/2202.02388/) (2022)

## Built on by (most cited first, 14 of 14)

- [PnP-Flow: Plug-and-Play Image Restoration with Flow Matching](https://mlsanity.com/paper/2410.02423/) (2024)
- [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)
- [Efficient Bayesian Computation Using Plug-and-Play Priors for Poisson Inverse Problems](https://mlsanity.com/paper/2503.16222/) (2025)
- [Compressive Recovery of Sparse Precision Matrices](https://mlsanity.com/paper/2311.04673/) (2023)
- [Measurement-Consistent Langevin Corrector for Stabilizing Latent Diffusion Inverse Problem Solvers](https://mlsanity.com/paper/2601.04791/) (2026)
- [RELD: Regularization by Latent Diffusion Models for Image Restoration](https://mlsanity.com/paper/2503.22563/) (2025)
- [PG-DPIR: An efficient plug-and-play method for high-count Poisson-Gaussian inverse problems](https://mlsanity.com/paper/2504.10375/) (2025)
- [Entropic Mirror Descent for Linear Systems: Polyak's Stepsize and Implicit Bias](https://mlsanity.com/paper/2505.02614/) (2025)
- [Bregman geometry-aware split Gibbs sampling for Bayesian Poisson inverse problems](https://mlsanity.com/paper/2511.12257/) (2025)
- [External Division of Two Bregman Proximity Operators for Poisson Inverse Problems](https://mlsanity.com/paper/2602.11482/) (2026)
- [A convergent Plug-and-Play Majorization-Minimization algorithm for Poisson inverse problems](https://mlsanity.com/paper/2603.24156/) (2026)
- [Self-Tuning Regularization for Image Scanning Microscopy](https://mlsanity.com/paper/2605.31426/) (2026)
- [A geometry-based deep equilibrium model for image restoration under multiplicative Gamma noise](https://mlsanity.com/paper/2608.04944/) (2026)

## Abstract (arXiv)

Plug-and-Play (PnP) methods are efficient iterative algorithms for solving ill-posed image inverse problems. PnP methods are obtained by using deep Gaussian denoisers instead of the proximal operator or the gradient-descent step within proximal algorithms. Current PnP schemes rely on data-fidelity terms that have either Lipschitz gradients or closed-form proximal operators, which is not applicable to Poisson inverse problems. Based on the observation that the Gaussian noise is not the adequate noise model in this setting, we propose to generalize PnP using theBregman Proximal Gradient (BPG) method. BPG replaces the Euclidean distance with a Bregman divergence that can better capture the smoothness properties of the problem. We introduce the Bregman Score Denoiser specifically parametrized and trained for the new Bregman geometry and prove that it corresponds to the proximal operator of a nonconvex potential. We propose two PnP algorithms based on the Bregman Score Denoiser for solving Poisson inverse problems. Extending the convergence results of BPG in the nonconvex settings, we show that the proposed methods converge, targeting stationary points of an explicit global functional. Experimental evaluations conducted on various Poisson inverse problems validate the convergence results and showcase effective restoration performance.