mlsanityData to 7 Oct 2026

Convolutional Proximal Neural Networks and Plug-and-Play Algorithms

arXiv 2011.02281 ↗First posted 4 Nov 2020math.OC cs.LG eess.SPcited by 36

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Abstract (arXiv)

In this paper, we introduce convolutional proximal neural networks (cPNNs), which are by construction averaged operators. For filters of full length, we propose a stochastic gradient descent algorithm on a submanifold of the Stiefel manifold to train cPNNs. In case of filters with limited length, we design algorithms for minimizing functionals that approximate the orthogonality constraints imposed on the operators by penalizing the least squares distance to the identity operator. Then, we investigate how scaled cPNNs with a prescribed Lipschitz constant can be used for denoising signals and images, where the achieved quality depends on the Lipschitz constant. Finally, we apply cPNN based denoisers within a Plug-and-Play (PnP) framework and provide convergence results for the corresponding PnP forward-backward splitting algorithm based on an oracle construction.

Key facts. Cited by 36 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Nov 2020.

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Citing papers per year: 2021: 4; 2022: 8; 2023: 8; 2024: 4; 2025: 9; 2026: 3.

36 papers.

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  1. 2021Gradient Step Denoiser for convergent Plug-and-Playcited by 107
  2. 2024PnP-Flow: Plug-and-Play Image Restoration with Flow Matchingcited by 92
  3. 2023Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --cited by 71
  4. 2022A Neural-Network-Based Convex Regularizer for Inverse Problemscited by 40
  5. 2021Generalized Normalizing Flows via Markov Chainscited by 23
  6. 2022Improving Lipschitz-Constrained Neural Networks by Learning Activation Functionscited by 23
  7. 2022PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularizationcited by 22
  8. 2022Approximation of Lipschitz Functions using Deep Spline Neural Networkscited by 15
  9. 2023Provably Convergent Plug-and-Play Quasi-Newton Methodscited by 15
  10. 2021Wasserstein Patch Prior for Image Superresolutioncited by 13
  11. 2023A relaxed proximal gradient descent algorithm for convergent plug-and-play with proximal denoisercited by 12
  12. 2025Learning Regularization Functionals for Inverse Problems: A Comparative Studycited by 12
24 more
  1. 2021Generalization Error Bounds for Iterative Recovery Algorithms Unfolded as Neural Networkscited by 11
  2. 2022WPPNets and WPPFlows: The Power of Wasserstein Patch Priors for Superresolutioncited by 10
  3. 2022Dynamical systems' based neural networkscited by 10
  4. 2023Designing Stable Neural Networks using Convex Analysis and ODEscited by 10
  5. 2023Prior Mismatch and Adaptation in PnP-ADMM with a Nonconvex Convergence Analysiscited by 10
  6. 2022Bayesian Inversion for Nonlinear Imaging Models using Deep Generative Priorscited by 9
  7. 2025An Adaptive Orthogonal Convolution Scheme for Efficient and Flexible CNN Architecturescited by 8
  8. 2025Approximation theory for 1-Lipschitz ResNetscited by 7
  9. 2025DEALing with Image Reconstruction: Deep Attentive Least Squarescited by 6
  10. 2022Proximal Residual Flows for Bayesian Inverse Problemscited by 5
  11. 2023Convergent plug-and-play with proximal denoiser and unconstrained regularization parametercited by 5
  12. 2024Stability of Data-Dependent Ridge-Regularization for Inverse Problemscited by 5
  13. 2025MAP Estimation with Denoisers: Convergence Rates and Guaranteescited by 5
  14. 2023NF-ULA: Langevin Monte Carlo with Normalizing Flow Prior for Imaging Inverse Problemscited by 4
  15. 2023How Much Training Data is Memorized in Overparameterized Autoencoders? An Inverse Problem Perspective on Memorization Evaluationcited by 2
  16. 2024Parseval Convolution Operators and Neural Networkscited by 2
  17. 2024Invertible ResNets for Inverse Imaging Problems: Competitive Performance with Provable Regularization Propertiescited by 2
  18. 2025Reconstruct Anything Model: a lightweight general model for computational imagingcited by 1
  19. 2025Universal Architectures for the Learning of Polyhedral Norms and Convex Regularizerscited by 1
  20. 2025Deep Network Trainability via Persistent Subspace Orthogonalitycited by 0
  21. 2025Stable neural networks and connections to continuous dynamical systemscited by 0
  22. 2026Domain Adaptation of Mismatched Proximal Denoiser for Plug-and-Play Image Reconstructioncited by 0
  23. 2026Stabilizing Deep Reconstruction Operators with Contractive Anchoringcited by 0
  24. 2026Trainable Nonexpansive Denoisers for Contractive Image Reconstructioncited by 0