# Tuning-free Plug-and-Play Proximal Algorithm for Inverse Imaging Problems

arXiv: https://arxiv.org/abs/2002.09611 · HTML: https://mlsanity.com/paper/2002.09611/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2020.

## Built on by (most cited first, 30 of 38)

- [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)
- [DSFormer: A Dual-domain Self-supervised Transformer for Accelerated Multi-contrast MRI Reconstruction](https://mlsanity.com/paper/2201.10776/) (2022)
- [Accelerating Quadratic Optimization with Reinforcement Learning](https://mlsanity.com/paper/2107.10847/) (2021)
- [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)
- [Deep Plug-and-Play Prior for Hyperspectral Image Restoration](https://mlsanity.com/paper/2209.08240/) (2022)
- [Graph Signal Restoration Using Nested Deep Algorithm Unrolling](https://mlsanity.com/paper/2106.15910/) (2021)
- [Prior Mismatch and Adaptation in PnP-ADMM with a Nonconvex Convergence Analysis](https://mlsanity.com/paper/2310.00133/) (2023)
- [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)
- [Gradient Importance Learning for Incomplete Observations](https://mlsanity.com/paper/2107.01983/) (2021)
- [Preconditioned Plug-and-Play ADMM with Locally Adjustable Denoiser for Image Restoration](https://mlsanity.com/paper/2110.00493/) (2021)
- [PnP-ReG: Learned Regularizing Gradient for Plug-and-Play Gradient Descent](https://mlsanity.com/paper/2204.13940/) (2022)
- [CurvPnP: Plug-and-play Blind Image Restoration with Deep Curvature Denoiser](https://mlsanity.com/paper/2211.07286/) (2022)
- [FiRe: Fixed-points of Restoration Priors for Solving Inverse Problems](https://mlsanity.com/paper/2411.18970/) (2024)
- [Deep Equilibrium Models for Video Snapshot Compressive Imaging](https://mlsanity.com/paper/2201.06931/) (2022)
- [Undersampled MRI Reconstruction with Side Information-Guided Normalisation](https://mlsanity.com/paper/2203.03196/) (2022)
- [Transitional Learning: Exploring the Transition States of Degradation for Blind Super-resolution](https://mlsanity.com/paper/2103.15290/) (2021)
- [Dynamic Proximal Unrolling Network for Compressive Imaging](https://mlsanity.com/paper/2107.11007/) (2021)
- [Tuning-free Plug-and-Play Hyperspectral Image Deconvolution with Deep Priors](https://mlsanity.com/paper/2211.15307/) (2022)
- [Phase Retrieval using Expectation Consistent Signal Recovery Algorithm based on Hypernetwork](https://mlsanity.com/paper/2101.04348/) (2021)
- [Single-Shot Plug-and-Play Methods for Inverse Problems](https://mlsanity.com/paper/2311.13682/) (2023)
- [Radio Map Estimation via Latent Domain Plug-and-Play Denoising](https://mlsanity.com/paper/2501.13472/) (2025)
- [DDPG-Driven Deep-Unfolding with Adaptive Depth for Channel Estimation with Sparse Bayesian Learning](https://mlsanity.com/paper/2201.08477/) (2022)
- [LoFi: Neural Local Fields for Scalable Image Reconstruction](https://mlsanity.com/paper/2411.04995/) (2024)
- [You KAN Do It in a Single Shot: Plug-and-Play Methods with Single-Instance Priors](https://mlsanity.com/paper/2412.06204/) (2024)
- [DDRM-PR: Fourier Phase Retrieval using Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2501.03030/) (2025)
- [Plug-and-Play Posterior Sampling for Blind Inverse Problems](https://mlsanity.com/paper/2505.22923/) (2025)
- [Alternative design of DeepPDNet in the context of image restoration](https://mlsanity.com/paper/2202.09810/) (2022)

## Abstract (arXiv)

Plug-and-play (PnP) is a non-convex framework that combines ADMM or other proximal algorithms with advanced denoiser priors. Recently, PnP has achieved great empirical success, especially with the integration of deep learning-based denoisers. However, a key problem of PnP based approaches is that they require manual parameter tweaking. It is necessary to obtain high-quality results across the high discrepancy in terms of imaging conditions and varying scene content. In this work, we present a tuning-free PnP proximal algorithm, which can automatically determine the internal parameters including the penalty parameter, the denoising strength and the terminal time. A key part of our approach is to develop a policy network for automatic search of parameters, which can be effectively learned via mixed model-free and model-based deep reinforcement learning. We demonstrate, through numerical and visual experiments, that the learned policy can customize different parameters for different states, and often more efficient and effective than existing handcrafted criteria. Moreover, we discuss the practical considerations of the plugged denoisers, which together with our learned policy yield state-of-the-art results. This is prevalent on both linear and nonlinear exemplary inverse imaging problems, and in particular, we show promising results on Compressed Sensing MRI and phase retrieval.