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Plug-and-Play Methods Provably Converge with Properly Trained Denoisers [article]

Ernest K. Ryu and Jialin Liu and Sicheng Wang and Xiaohan Chen and Zhangyang Wang and Wotao Yin
2019 arXiv   pre-print
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.  ...  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.  ...  Acknowledgements We thank Pontus Giselsson for the discussion on negatively averaged operators and Stanley Chan for the discussion on the difficulties in establishing convergence of PnP methods.  ... 
arXiv:1905.05406v1 fatcat:yug6odaxubgrbej57h2owtnszy

Denoising Score-Matching for Uncertainty Quantification in Inverse Problems [article]

Zaccharie Ramzi, Benjamin Remy, Francois Lanusse, Jean-Luc Starck, Philippe Ciuciu
2020 arXiv   pre-print
We adopt recent denoisingscore matching techniques to learn this prior from data, and subsequently use it aspart of an annealed Hamiltonian Monte-Carlo scheme to sample the full posteriorof image inverse  ...  We apply this framework to Magnetic ResonanceImage (MRI) reconstruction and illustrate how this approach not only yields highquality reconstructions but can also be used to assess the uncertainty on particularfeatures  ...  Acknowledgments and Disclosure of Funding We acknowledge the financial support of the Cross-Disciplinary Program on Numerical Simulation of CEA for the project entitled SILICOSMIC.  ... 
arXiv:2011.08698v1 fatcat:ukjxwlxnffbjvhn5vq6mf3u3ui

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

Kaixuan Wei, Angelica Aviles-Rivero, Jingwei Liang, Ying Fu, Hua Huang, Carola-Bibiane Schönlieb
2021 arXiv   pre-print
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.  ...  Moreover, we discuss several practical considerations of PnP denoisers, which together with our learned policy yield state-of-the-art results.  ...  Authors also gratefully acknowledge the financial support of the CMIH and CCIMI University of Cambridge, and Graduate school of Beijing Institute of Technology.  ... 
arXiv:2012.05703v3 fatcat:jcwekn62ira73lf5etemy3vd2q

Model-based Reconstruction with Learning: From Unsupervised to Supervised and Beyond [article]

Zhishen Huang and Siqi Ye and Michael T. McCann and Saiprasad Ravishankar
2021 arXiv   pre-print
Model-based reconstruction methods have been particularly popular (e.g., in magnetic resonance imaging and tomographic modalities) and exploit models of the imaging system's physics together with statistical  ...  We briefly discuss classical model-based reconstruction methods and then review reconstruction methods at the intersection of model-based and learning-based paradigms in detail.  ...  supervised way) and CNN-based plug-and-play methods.  ... 
arXiv:2103.14528v1 fatcat:kxzugqnnijdwfn62jwrl45zmge

Bayesian imaging using Plug Play priors: when Langevin meets Tweedie [article]

Rémi Laumont, Valentin de Bortoli, Andrés Almansa, Julie Delon, Alain Durmus, Marcelo Pereyra
2022 arXiv   pre-print
To address these limitations, this paper develops theory, methods, and provably convergent algorithms for performing Bayesian inference with PnP priors.  ...  Since the seminal work of Venkatakrishnan et al. in 2013, Plug & Play (PnP) methods have become ubiquitous in Bayesian imaging.  ...  The Plug & Play ULA methods studied in this paper are closely related to (5) , with a state-of-the-art Gaussian denoiser "plugged" in lieu of prox λ U .  ... 
arXiv:2103.04715v6 fatcat:4xryxmhvd5gvxa6xujnnp3d5w4

Learning to Optimize: A Primer and A Benchmark [article]

Tianlong Chen, Xiaohan Chen, Wuyang Chen, Howard Heaton, Jialin Liu, Zhangyang Wang, Wotao Yin
2021 arXiv   pre-print
The practicality of L2O depends on the type of target optimization, the chosen architecture of the method to learn, and the training procedure.  ...  It automates the design of an optimization method based on its performance on a set of training problems.  ...  Emphases are given to recurrent network-based L2O methods, algorithm unrolling, and plug-and-play.  ... 
arXiv:2103.12828v2 fatcat:c75y3wz6cngirb2zpugjk63ymq

Regularization by Denoising via Fixed-Point Projection (RED-PRO) [article]

Regev Cohen, Michael Elad, Peyman Milanfar
2020 arXiv   pre-print
A recent regularization strategy of great interest utilizes the power of denoising engines. Two such methods are the Plug-and-Play Prior (PnP) and Regularization by Denoising (RED).  ...  In addition, we present relaxations of RED-PRO that allow for handling denoisers with limited fixed-point sets.  ...  The first to propose leveraging the power of denoising for regularization were Venkatakrishnan et al., presenting their Plug-and-Play Prior (PnP) framework [92, 22, 82] .  ... 
arXiv:2008.00226v2 fatcat:qbjpach67jfjfiyeddw2zu3xjq

Model-Based Deep Learning [article]

Nir Shlezinger, Jay Whang, Yonina C. Eldar, Alexandros G. Dimakis
2021 arXiv   pre-print
Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and additional domain knowledge.  ...  We provide a comprehensive review of the leading approaches for combining model-based algorithms with deep learning in a systematic manner, along with concrete guidelines and detailed signal processing  ...  As this approach can also utilize model-based denoisers, we use the term plug-and-play networks for such methods with DNN-based denoisers.  ... 
arXiv:2012.08405v2 fatcat:4ilqi3vv4rar5gsveqzo4loqpy

Robust Blind Deconvolution via Mirror Descent [article]

Sathya N. Ravi, Ronak Mehta, Vikas Singh
2018 arXiv   pre-print
We revisit the Blind Deconvolution problem with a focus on understanding its robustness and convergence properties.  ...  The algorithm that emerges has nice convergence guarantees and is provably robust in a sense we formalize in the paper.  ...  This immediately entails that with with very high probability, a gradient method will converge to a local minimizer.  ... 
arXiv:1803.08137v1 fatcat:o2dtouwyrjc5hchv3cjoioghba

Deep Learning Techniques for Inverse Problems in Imaging [article]

Gregory Ongie, Ajil Jalal, Christopher A. Metzler, Richard G. Baraniuk, Alexandros G. Dimakis, Rebecca Willett
2020 arXiv   pre-print
We explore the central prevailing themes of this emerging area and present a taxonomy that can be used to categorize different problems and reconstruction methods.  ...  We also discuss the trade-offs associated with these different reconstruction approaches, caveats and common failure modes, plus open problems and avenues for future work.  ...  This includes compressed sensing with generative models and iterative plug-and-play reconstruction with a denoising autoencoder.  ... 
arXiv:2005.06001v1 fatcat:z7w3vygugjf57fqbe6t62fvni4

Augmented NETT Regularization of Inverse Problems [article]

Daniel Obmann, Linh Nguyen, Johannes Schwab, Markus Haltmeier
2021 arXiv   pre-print
We propose a possible realization together with a network architecture and a modular training strategy.  ...  We present a rigorous convergence analysis including stability estimates and convergence rates.  ...  While convergence of (S1)-(S3) and relations with plug and play priors are interesting and relevant, they are beyond the scope of this work.  ... 
arXiv:1908.03006v3 fatcat:ay6bu6gykva5zkyk2tie7zqztu

Skew Orthogonal Convolutions [article]

Sahil Singla, Soheil Feizi
2021 arXiv   pre-print
Training convolutional neural networks with a Lipschitz constraint under the l_2 norm is useful for provable adversarial robustness, interpretable gradients, stable training, etc.  ...  Our experiments on CIFAR-10 and CIFAR-100 show that SOC allows us to train provably Lipschitz, large convolutional neural networks significantly faster than prior works while achieving significant improvements  ...  ., and Yin, W. Plug-and-play methods provably converge with properly trained denoisers. In Chaudhuri, K. and Salakhutdinov, R.  ... 
arXiv:2105.11417v2 fatcat:4cwida6vonejpmnfzplubejfnq

Deep Learning of Representations: Looking Forward [chapter]

Yoshua Bengio
2013 Lecture Notes in Computer Science  
Abstract Recent work has shown how denoising and contractive autoencoders implicitly capture the structure of the data-generating density, in the case where the corruption noise is Gaussian, the reconstruction  ...  However, it remained unclear how to connect the training procedure of regularized auto-encoders to the implicit estimation of the underlying datagenerating distribution when the data are discrete, or using  ...  Acknowledgments The author is extremely grateful for the feedback and discussions he enjoyed with collaborators Ian Goodfellow, Guillaume Desjardins, Aaron Courville, Pascal Vincent, Roland Memisevic and  ... 
doi:10.1007/978-3-642-39593-2_1 fatcat:xad2okhdkrfbrhe4ilujsnoqlu

Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learning [article]

Saiprasad Ravishankar, Jong Chul Ye, Jeffrey A. Fessler
2019 arXiv   pre-print
A fourth type of methods replaces mathematically designed models of signals and systems with data-driven or adaptive models inspired by the field of machine learning.  ...  A third type of methods has been designed to accommodate modified data acquisition methods, such as reduced sampling in MRI and CT to reduce scan time or radiation dose.  ...  Rather than using a CNN penalty explicitly, in the plug-and-play approach [171] , [172] , the denoising step of an iteration like ADMM is replaced with a neural network denoiser.  ... 
arXiv:1904.02816v2 fatcat:ehahzrib2ff3dl5yl6pa7xpf24

Solving inverse problems using data-driven models

Simon Arridge, Peter Maass, Ozan Öktem, Carola-Bibiane Schönlieb
2019 Acta Numerica  
Recent research in inverse problems seeks to develop a mathematically coherent foundation for combining data-driven models, and in particular those based on deep learning, with domain-specific knowledge  ...  The focus is on solving ill-posed inverse problems that are at the core of many challenging applications in the natural sciences, medicine and life sciences, as well as in engineering and industrial applications  ...  Acknowledgements This article builds on lengthy discussions and long-standing collaborations with a large number of people.  ... 
doi:10.1017/s0962492919000059 fatcat:2f7te542wrftphdhurcdnw6dqu
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