[Paper Review] TFPnP: Tuning-free Plug-and-Play Proximal Algorithm with Applications to Inverse Imaging Problems

Kaixuan Wei, Angelica I. Avilés-Rivero+4 more|arXiv (Cornell University)|Nov 18, 2020

Sparse and Compressive Sensing Techniques207 references4 citations

TL;DR

This paper proposes TFPnP, a tuning-free plug-and-play proximal algorithm that uses a hybrid reinforcement learning policy network to automatically optimize denoising strength, termination time, and other parameters in inverse imaging problems. The method achieves state-of-the-art performance across linear and nonlinear imaging tasks, including compressed sensing MRI and sparse-view CT, by learning to Gaussianize iteration noise and outperforming handcrafted and oracle-based parameter settings.

ABSTRACT

Plug-and-Play (PnP) is a non-convex optimization framework that combines proximal algorithms, for example, the alternating direction method of multipliers (ADMM), with advanced denoising priors. Over the past few years, great empirical success has been obtained by PnP algorithms, especially for the ones that integrate deep learning-based denoisers. However, a key challenge of PnP approaches is the need for manual parameter tweaking as it is essential to obtain high-quality results across the high discrepancy in imaging conditions and varying scene content. In this work, we present a class of tuning-free PnP proximal algorithms that can determine parameters such as denoising strength, termination time, and other optimization-specific parameters automatically. A core part of our approach is a policy network for automated parameter search which can be effectively learned via a mixture of model-free and model-based deep reinforcement learning strategies. We demonstrate, through rigorous numerical and visual experiments, that the learned policy can customize parameters to different settings, and is often more efficient and effective than existing handcrafted criteria. Moreover, we discuss several practical considerations of PnP denoisers, which together with our learned policy yield state-of-the-art results. This advanced performance is prevalent on both linear and nonlinear exemplar inverse imaging problems, and in particular shows promising results on compressed sensing MRI, sparse-view CT, single-photon imaging, and phase retrieval.

Motivation & Objective

• To address the critical challenge of manual parameter tuning in plug-and-play (PnP) proximal algorithms for inverse imaging problems.
• To develop a tuning-free framework that automatically determines denoising strength, termination time, and optimization-specific parameters.
• To improve the robustness and efficiency of PnP methods across diverse imaging conditions and scene content.
• To investigate the statistical properties of iteration noise in PnP algorithms and leverage them for better performance.
• To achieve state-of-the-art reconstruction quality without relying on handcrafted or oracle-tuned parameters.

Proposed method

• A hybrid reinforcement learning policy network is trained using a mixture of model-free and model-based deep reinforcement learning strategies.
• The policy network learns to select optimal parameters—such as denoising strength and stopping time—based on image and noise characteristics.
• The method leverages the normality of iteration noise, which is Gaussianized over iterations, to improve denoising effectiveness.
• The policy is trained via a reward function that maximizes PSNR and minimizes residual error, with feedback from the PnP algorithm's convergence behavior.
• The framework integrates with standard proximal algorithms like ADMM and PGM, enabling plug-and-play use with any denoiser.
• Empirical analysis uses Gaussian probability plots and R² to evaluate the normality of iteration noise, which correlates with reconstruction quality.

Experimental results

Research questions

• RQ1 Can a learned policy automatically determine optimal denoising strength and termination time in PnP proximal algorithms without manual tuning?
• RQ2 How does the normality of iteration noise evolve during PnP iterations, and can it be leveraged to improve reconstruction quality?
• RQ3 Can a reinforcement learning-based policy outperform handcrafted and oracle-tuned parameter settings in diverse inverse imaging scenarios?
• RQ4 To what extent does Gaussianizing iteration noise enhance the performance of PnP methods across different imaging modalities?
• RQ5 How scalable and generalizable is the proposed policy network across linear and nonlinear inverse imaging problems?

Key findings

• The learned policy achieves PSNR of 26.41 on PnP-ADMM, outperforming the oracle policy in some settings and matching or exceeding handcrafted criteria.
• PnP-ADMM shows the highest improvement in iteration noise normality, with an R² of 0.972, correlating with superior reconstruction quality.
• The method significantly improves PSNR and normality of iteration noise compared to fixed and oracle policies, especially in challenging tasks like compressed sensing MRI and single-photon imaging.
• The policy network effectively generalizes across diverse imaging conditions and scene content, reducing the need for manual parameter tuning.
• A strong positive correlation is observed between the R² of Gaussian probability plots (measuring noise normality) and PSNR, validating the importance of Gaussianizing iteration noise.
• The framework achieves state-of-the-art results on exemplar inverse imaging problems, including sparse-view CT and phase retrieval, with minimal user intervention.