Plug-and-Play Methods Provably Converge with Properly Trained Denoisers

By Ernest K. Ryu, Jialin Liu, Sicheng Wang, Xiaohan Chen, Zhangyang Wang, Wotao Yin. International Conference on Machine Learning, 2019

451 citations recorded by the source corpus.

Plug-and-play (PnP) is a non-convex framework that integrates modern denoising priors, such as BM3D or deep learning-based denoisers, into ADMM or other proximal algorithms. An advantage of PnP is that one can use pre-trained denoisers when there is not sufficient data for end-to-end training. Although PnP has been recently studied extensively with great empirical success, theoretical analysis addressing even the most basic question of convergence has been insufficient. In this paper, we theoretically establish convergence of PnP-FBS and PnP-ADMM, without using diminishing stepsizes, under a certain Lipschitz condition on the denoisers. We then propose real spectral normalization, a technique for training deep learning-based denoisers to satisfy the proposed Lipschitz condition. Finally, we present experimental results validating the theory.

Subfields: Artificial Intelligence, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/e74c8596ea08ef5e366ffdde330ccd6a13284f65

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Wuyang Chen
2. Zhangyang Wang
3. Tianlong Chen
4. Yonina C. Eldar
5. Kai Zhang
6. Aggelos K. Katsaggelos
7. Jingyun Liang
8. Luc Van Gool

In Computational Mechanics

1. Radu Timofte
2. Luc Van Gool
3. Xin Yuan
4. Aggelos K. Katsaggelos
5. David J. Brady
6. Jingyun Liang
7. Kai Zhang
8. Zhangyang Wang

In Computer Vision and Pattern Recognition

1. Luc Van Gool
2. Radu Timofte
3. Kai Zhang
4. Zhangyang Wang
5. Jingyun Liang
6. Lei Zhang
7. Chen Change Loy
8. Ming-Hsuan Yang

Citations in the corpus

• Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing (2019, background): “[101] prove that, when the denoisers satisfy certain Lipschitz conditions, replacing the proximal operators with denoisers leads to convergence for some popular optimization algorithms such as ADMM and forward-backward splitting.”
• Denoising Diffusion Models for Plug-and-Play Image Restoration (2023, background): “In particular, the prior term can be implicitly addressed by Gaussian denois-ers [39, 47, 54, 60].”
• Learning to Optimize: A Primer and A Benchmark (2021, background): “[179] studied the convergence of some PnP frameworks using fixed-point iterations, showing guaranteed convergence under a certain Lipschitz condition on the denoisers.”
• Snapshot Compressive Imaging: Theory, Algorithms, and Applications (2021, background): “Moreover, the convergence results [98] can be obtained by appropriate assumptions, e.”
• Deep Generalized Unfolding Networks for Image Restoration (2022, methodology): “Such correspondence was originally applied in deep plugand-play (PNP) methods [44, 57, 74, 92, 94], which utilize trained denoiser to implicitly express the regularization term J(x) as a denoising problem.”