Building Firmly Nonexpansive Convolutional Neural Networks

Terris, Matthieu; Repetti, Audrey; Pesquet, Jean-Christophe; Wiaux, Yves

doi:10.1109/icassp40776.2020.9054731

Cited by 29 publications

(22 citation statements)

References 16 publications

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“…Prior work has also shown that Lipschitz constrained residual networks yield excellent performance without sacrificing stable convergence [23], [46]. Additionally, there has recently been an explosion of techniques for training Lipschitz constrained and firmly nonexpansive deep neural nets [23], [64]- [66].…”

Section: B Convergence Analysismentioning

confidence: 99%

Scalable Plug-and-Play ADMM With Convergence Guarantees

Sun

et al. 2021

IEEE Trans. Comput. Imaging

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Plug-and-play priors (PnP) is a broadly applicable methodology for solving inverse problems by exploiting statistical priors specified as denoisers. Recent work has reported the stateof-the-art performance of PnP algorithms using pre-trained deep neural nets as denoisers in a number of imaging applications. However, current PnP algorithms are impractical in large-scale settings due to their heavy computational and memory requirements. This work addresses this issue by proposing an incremental variant of the widely used PnP-ADMM algorithm, making it scalable to large-scale datasets. We theoretically analyze the convergence of the algorithm under a set of explicit assumptions, extending recent theoretical results in the area. Additionally, we show the effectiveness of our algorithm with nonsmooth datafidelity terms and deep neural net priors, its fast convergence compared to existing PnP algorithms, and its scalability in terms of speed and memory.

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Section: B Convergence Analysismentioning

confidence: 99%

Scalable Plug-and-Play ADMM With Convergence Guarantees

Sun

et al. 2021

IEEE Trans. Comput. Imaging

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“…PnP methods have been successfully applied in the literature with various splitting schemes: HQS (Zhang et al, 2017b;, ADMM (Romano et al, 2017;Ryu et al, 2019), Proximal Gradient Descent (PGD) (Terris et al, 2020). First used with classical non deep denoisers such as BM3D (Chan et al, 2016) and pseudo-linear denoisers (Nair et al, 2021;, more recent PnP approaches (Meinhardt et al, 2017;Ryu et al, 2019) rely on efficient off-theshelf deep denoisers such as DnCNN (Zhang et al, 2017a).…”

Section: Related Workmentioning

confidence: 99%

“…Sreehari et al (2016) first used the proximal theorem of Moreau (Moreau, 1965) to give sufficient conditions for the denoiser to be an exact proximal map, which are applied to a pseudo-linear denoiser. The convergence with pseudo-linear denoisers have then been extensively studied (Gavaskar & Chaudhury, 2020;Nair et al, 2021;Chan, 2019) (Sun et al, 2019), firmly nonexpansive (Sun et al, 2021;Terris et al, 2020) or simply a nonexpansive (Reehorst & Schniter, 2018;Liu et al, 2021). These settings are unrealistic as deep denoisers do not generally satisfy such properties.…”

Section: Related Workmentioning

confidence: 99%

Gradient Step Denoiser for convergent Plug-and-Play

Hurault¹,

Leclaire²,

Papadakis³

2021

Preprint

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Plug-and-Play methods constitute a class of iterative algorithms for imaging problems where regularization is performed by an off-the-shelf denoiser. Although Plug-and-Play methods can lead to tremendous visual performance for various image problems, the few existing convergence guarantees are based on unrealistic (or suboptimal) hypotheses on the denoiser, or limited to strongly convex data terms. In this work, we propose a new type of Plug-and-Play methods, based on half-quadratic splitting, for which the denoiser is realized as a gradient descent step on a functional parameterized by a deep neural network. Exploiting convergence results for proximal gradient descent algorithms in the non-convex setting, we show that the proposed Plug-and-Play algorithm is a convergent iterative scheme that targets stationary points of an explicit global functional. Besides, experiments show that it is possible to learn such a deep denoiser while not compromising the performance in comparison to other state-of-the-art deep denoisers used in Plug-and-Play schemes. We apply our proximal gradient algorithm to various ill-posed inverse problems, e.g. deblurring, super-resolution and inpainting. For all these applications, numerical results empirically confirm the convergence results. Experiments also show that this new algorithm reaches state-of-the-art performance, both quantitatively and qualitatively. 1

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“…The theoretical convergence of sequences generated by PnP algorithms has drawn a lot of attention in the last years [12,13,14,15]. However, it often relies on strong structural constraints on the denoiser (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…However, it often relies on strong structural constraints on the denoiser (e.g. NNs without residual skip connection) [14,15], and/or the limit point is not clearly characterized [12,13].…”

Section: Introductionmentioning

confidence: 99%

Enhanced Convergent PNP Algorithms For Image Restoration

Terris

Repetti

Pesquet³

et al. 2021

2021 IEEE International Conference on Image Processing (ICIP)

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Image restoration has long been one of the key research topics in image processing. Many mathematical approaches have been developed to solve this problem, e.g., variational methods, wavelet techniques, or Bayesian methods. With the widespread of neural network (NN) models in all the subdomains of data science, the performance limits of these methods are further pushed. One of the most successful strategies consists of plugging NNs in existing optimization algorithms. However, so doing raises several mathematical and practical challenges. One of the main issues is to secure the convergence of the resulting iterative scheme. Further questions concerning the characterization of the reached limit are also worth being addressed. In this paper, we show that the theory of maximally monotone operators allows us to bring insightful answers to these problems and to design firmly nonexpansive NNs; combining these with postprocessing NNs leads to excellent global restoration quality.

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Building Firmly Nonexpansive Convolutional Neural Networks

Cited by 29 publications

References 16 publications

Scalable Plug-and-Play ADMM With Convergence Guarantees

Scalable Plug-and-Play ADMM With Convergence Guarantees

Gradient Step Denoiser for convergent Plug-and-Play

Enhanced Convergent PNP Algorithms For Image Restoration

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