# Scalable Plug-and-Play ADMM with Convergence Guarantees

arXiv: https://arxiv.org/abs/2006.03224 · HTML: https://mlsanity.com/paper/2006.03224/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2020.

## Built on by (most cited first, 30 of 50)

- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (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)
- [Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --](https://mlsanity.com/paper/2301.03362/) (2023)
- [Provable Probabilistic Imaging using Score-Based Generative Priors](https://mlsanity.com/paper/2310.10835/) (2023)
- [Recovery of Continuous 3D Refractive Index Maps from Discrete Intensity-Only Measurements using Neural Fields](https://mlsanity.com/paper/2112.00002/) (2021)
- [What's in a Prior? Learned Proximal Networks for Inverse Problems](https://mlsanity.com/paper/2310.14344/) (2023)
- [Improving Lipschitz-Constrained Neural Networks by Learning Activation Functions](https://mlsanity.com/paper/2210.16222/) (2022)
- [Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Condition](https://mlsanity.com/paper/2106.03668/) (2021)
- [Online Deep Equilibrium Learning for Regularization by Denoising](https://mlsanity.com/paper/2205.13051/) (2022)
- [Theoretical Perspectives on Deep Learning Methods in Inverse Problems](https://mlsanity.com/paper/2206.14373/) (2022)
- [Learning Image Priors through Patch-based Diffusion Models for Solving Inverse Problems](https://mlsanity.com/paper/2406.02462/) (2024)
- [Provably Convergent Plug-and-Play Quasi-Newton Methods](https://mlsanity.com/paper/2303.07271/) (2023)
- [On Maximum-a-Posteriori estimation with Plug & Play priors and stochastic gradient descent](https://mlsanity.com/paper/2201.06133/) (2022)
- [Convergent Bregman Plug-and-Play Image Restoration for Poisson Inverse Problems](https://mlsanity.com/paper/2306.03466/) (2023)
- [A relaxed proximal gradient descent algorithm for convergent plug-and-play with proximal denoiser](https://mlsanity.com/paper/2301.13731/) (2023)
- [Prior Mismatch and Adaptation in PnP-ADMM with a Nonconvex Convergence Analysis](https://mlsanity.com/paper/2310.00133/) (2023)
- [Bayesian Inversion for Nonlinear Imaging Models using Deep Generative Priors](https://mlsanity.com/paper/2203.10078/) (2022)
- [Deep Model-Based Architectures for Inverse Problems under Mismatched Priors](https://mlsanity.com/paper/2207.13200/) (2022)
- [Block Coordinate Plug-and-Play Methods for Blind Inverse Problems](https://mlsanity.com/paper/2305.12672/) (2023)
- [Patch-Based Diffusion Models Beat Whole-Image Models for Mismatched Distribution Inverse Problems](https://mlsanity.com/paper/2410.11730/) (2024)
- [Proximal Algorithm Unrolling: Flexible and Efficient Reconstruction Networks for Single-Pixel Imaging](https://mlsanity.com/paper/2505.23180/) (2025)
- [Memory-efficient model-based deep learning with convergence and robustness guarantees](https://mlsanity.com/paper/2206.04797/) (2022)
- [Deep Equilibrium models for Poisson Imaging Inverse problems via Mirror Descent](https://mlsanity.com/paper/2507.11461/) (2025)
- [A Plug-and-Play Approach to Multiparametric Quantitative MRI: Image Reconstruction using Pre-Trained Deep Denoisers](https://mlsanity.com/paper/2202.05269/) (2022)
- [CoRRECT: A Deep Unfolding Framework for Motion-Corrected Quantitative R2* Mapping](https://mlsanity.com/paper/2210.06330/) (2022)
- [Convergent plug-and-play with proximal denoiser and unconstrained regularization parameter](https://mlsanity.com/paper/2311.01216/) (2023)
- [Plug-and-Play Priors as a Score-Based Method](https://mlsanity.com/paper/2412.11108/) (2024)
- [MAP Estimation with Denoisers: Convergence Rates and Guarantees](https://mlsanity.com/paper/2507.15397/) (2025)
- [Unrolled Variational Bayesian Algorithm for Image Blind Deconvolution](https://mlsanity.com/paper/2110.07202/) (2021)

## Abstract (arXiv)

Plug-and-play priors (PnP) is a broadly applicable methodology for solving inverse problems by exploiting statistical priors specified as denoisers. Recent work has reported the state-of-the-art performance of PnP algorithms using pre-trained deep neural nets as denoisers in a number of imaging applications. However, current PnP algorithms are impractical in large-scale settings due to their heavy computational and memory requirements. This work addresses this issue by proposing an incremental variant of the widely used PnP-ADMM algorithm, making it scalable to large-scale datasets. We theoretically analyze the convergence of the algorithm under a set of explicit assumptions, extending recent theoretical results in the area. Additionally, we show the effectiveness of our algorithm with nonsmooth data-fidelity terms and deep neural net priors, its fast convergence compared to existing PnP algorithms, and its scalability in terms of speed and memory.