Plug-and-Play ADMM for Image Restoration: Fixed-Point Convergence and Applications

By Stanley H. Chan, Xiran Wang, Omar A. Elgendy. IEEE Transactions on Computational Imaging, 2016

918 citations recorded by the source corpus.

Alternating direction method of multiplier (ADMM) is a widely used algorithm for solving constrained optimization problems in image restoration. Among many useful features, one critical feature of the ADMM algorithm is its modular structure, which allows one to plug in any off-the-shelf image denoising algorithm for a subproblem in the ADMM algorithm. Because of the plug-in nature, this type of ADMM algorithms is coined the name “Plug-and-Play ADMM.” Plug-and-Play ADMM has demonstrated promising empirical results in a number of recent papers. However, it is unclear under what conditions and by using what denoising algorithms would it guarantee convergence. Also, since Plug-and-Play ADMM uses a specific way to split the variables, it is unclear if fast implementation can be made for common Gaussian and Poissonian image restoration problems. In this paper, we propose a Plug-and-Play ADMM algorithm with provable fixed-point convergence. We show that for any denoising algorithm satisfying an asymptotic criteria, called bounded denoisers, Plug-and-Play ADMM converges to a fixed point under a continuation scheme. We also present fast implementations for two image restoration problems on superresolution and single-photon imaging. We compare Plug-and-Play ADMM with state-of-the-art algorithms in each problem type and demonstrate promising experimental results of the algorithm.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/1dc8422156c87437b2b981b742b24ab530705bb7

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Citations in the corpus

Plug-and-Play Methods Provably Converge with Properly Trained Denoisers (2019, methodology): “(Chan et al., 2017) analyzed convergence with a bounded denoiser assumption, establishing convergence using an increasing penalty parameter.”
Learning to Optimize: A Primer and A Benchmark (2021, methodology): “Then [40] proved the convergence of PnP-ADMM with the use of a more realistic “bounded denoisers” assumption.”
Deep Plug-And-Play Super-Resolution for Arbitrary Blur Kernels (2019, methodology): “Moreover, different from existing plug-and-play framework [13] which generally plugs the off-the-shelf Gaussian denoiser as a modular part, the proposed instead achieves the plug-in step by applying any existing DNN-based super-resolvers with only a small modiﬁcation.”
MoDL: Model-Based Deep Learning Architecture for Inverse Problems (2017, methodology): “Note that the above formulation is very similar to the plug-and-play prior approach in [37]; the main difference is that the denoiser is a deep CNN in our setting, similar to [16].”
Denoising Diffusion Models for Plug-and-Play Image Restoration (2023, background): “Recent studies have demonstrated that plug-and-play Image Restoration (IR) methods can effectively handle a variety of low-level vision tasks, such as image denoising [5], image Super-Resolution (SR) [16, 17, 37], image deblurring [12] and image inpainting [27], with excellent results [6, 11, 54, 57”
Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolation (2015, background): “have adapted plug-and-play for a variety of image restoration problems [42], while Teodoro et al.”
Snapshot Compressive Imaging: Theory, Algorithms, and Applications (2021, methodology): “This has been further repurposed and generalized to the PnP [82] framework.”
FFDNet: Toward a Fast and Flexible Solution for CNN-Based Image Denoising (2017, background): “Thus, the non-blind model can be easily plugged into variable splitting algorithms to solve various image restoration tasks, such as image deblurring, SISR, and image inpainting [9], [48].”
Deep Unfolding Network for Image Super-Resolution (2020, background): “(6), it is known that, from a Bayesian perspective, it actually corresponds to a denoising problem with noise level βk , √ λ/μk [10].”
Diffusion Posterior Sampling for General Noisy Inverse Problems (2022, methodology): “4, we specifically compare our methods with DDRM and PnP-ADMM, which are two methods that are known to be robust to measurement noise.”
Deep Generalized Unfolding Networks for Image Restoration (2022, background): “(5b), it is known that, from a Bayesian perspective, it actually corresponds to a denoising problem [9,74].”
Denoising Prior Driven Deep Neural Network for Image Restoration (2018, methodology): “(2) can be rewritten as In [26], [30], the ADMM technique is used to convert the above equally constrained optimization problem into two sub-problems where u denotes the augmented Lagrange multiplier updated as u ( t +1) = u ( t ) + ρ ( x ( t +1) − v ( t +1) ) .”
Learning Deep CNN Denoiser Prior for Image Restoration (2017, background): “Some of the other related work can be found in [6, 12, 48, 49, 54, 58].”
Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems (2017, background): “Theoretical results including conditions under which the alternating directions method of multipliers (ADMM) with a custom proximal operator converges were presented in [31, 5].”
The Little Engine That Could: Regularization by Denoising (RED) (2016, positive): “This statement poses the proposed 476 algorithm as superior to the P 3 scheme, which at best is known to get to a stable-point 477 [30, 33,34].”