mlsanityData to 14 Oct 2026

Trainable Nonexpansive Denoisers for Contractive Image Reconstruction

arXiv 2607.23347 ↗First posted 25 Jul 2026eess.IV cs.CVcited by 0

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Abstract (arXiv)

Trainable denoisers with Lipschitz control have become central to convergent image reconstruction. However, training neural networks that simultaneously offer strong denoising performance and global Lipschitz guarantees is challenging. Existing approaches enforce Lipschitz control only empirically, providing no guarantees beyond the training data. In this work, we show that by exploiting the action of permutations on the image lattice, we can constrain a neural architecture that is globally nonexpansive (Lipschitz bound leqslant 1). We integrate the proposed denoiser with forward imaging operators to develop a reconstruction mechanism that is provably contractive and therefore globally convergent. Experiments on standard inverse problems, such as superresolution and deblurring, demonstrate that our reconstruction performance is competitive with softly constrained baselines while providing Lipschitz guarantees.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 24 of its 35 references that are in the map. First posted on arXiv 25 Jul 2026.

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24 of 35 references.

References · 24

  1. 2017Attention Is All You Needcited by 60,361
  2. 2017Non-local Neural Networkscited by 2,293
  3. 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,358
  4. 2022Denoising Diffusion Restoration Modelscited by 963
  5. 2020Plug-and-Play Image Restoration with Deep Denoiser Priorcited by 470
  6. 2018Lipschitz regularity of deep neural networks: analysis and efficient estimationcited by 415
  7. 2017Learning Deep CNN Denoiser Prior for Image Restorationcited by 408
  8. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 307
  9. 2019Residual Non-local Attention Networks for Image Restorationcited by 236
  10. 2019Plug-and-Play Methods Provably Converge with Properly Trained Denoiserscited by 198
  11. 2018Regularization by Denoising: Clarifications and New Interpretationscited by 103
  12. 2022Practical Blind Image Denoising via Swin-Conv-UNet and Data Synthesiscited by 86
12 more
  1. 2022Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularizationcited by 80
  2. 2015Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolationcited by 78
  3. 2023Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --cited by 71
  4. 2020Learning Maximally Monotone Operators for Image Recoverycited by 62
  5. 2019Basis Prediction Networks for Effective Burst Denoising with Large Kernelscited by 46
  6. 2022A Neural-Network-Based Convex Regularizer for Inverse Problemscited by 41
  7. 2020Convolutional Proximal Neural Networks and Plug-and-Play Algorithmscited by 36
  8. 2023Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithmscited by 31
  9. 2022Improving Lipschitz-Constrained Neural Networks by Learning Activation Functionscited by 24
  10. 2021On Plug-and-Play Regularization using Linear Denoiserscited by 9
  11. 2024Learning pseudo-contractive denoisers for inverse problemscited by 6
  12. 2025Learning Cocoercive Conservative Denoisers via Helmholtz Decomposition for Poisson Inverse Problemscited by 4

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