mlsanityData to 14 Oct 2026

Provably Convergent Data-Driven Convex-Nonconvex Regularization

arXiv 2310.05812 ↗First posted 9 Oct 2023cs.LG cs.CV stat.MLcited by 4

Not on the map. Why?

Abstract (arXiv)

An emerging new paradigm for solving inverse problems is via the use of deep learning to learn a regularizer from data. This leads to high-quality results, but often at the cost of provable guarantees. In this work, we show how well-posedness and convergent regularization arises within the convex-nonconvex (CNC) framework for inverse problems. We introduce a novel input weakly convex neural network (IWCNN) construction to adapt the method of learned adversarial regularization to the CNC framework. Empirically we show that our method overcomes numerical issues of previous adversarial methods.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 22 of its 42 references that are in the map. First posted on arXiv 9 Oct 2023.

Builds on

22 of 42 references.

References · 22

  1. 2017Deep Image Priorcited by 1,098
  2. 2016Deep Convolutional Neural Network for Inverse Problems in Imagingcited by 433
  3. 2016Input Convex Neural Networkscited by 414
  4. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 307
  5. 2017Learned Primal-dual Reconstructioncited by 251
  6. 2016Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applicationscited by 246
  7. 2019Plug-and-Play Methods Provably Converge with Properly Trained Denoiserscited by 198
  8. 2021Gradient Step Denoiser for convergent Plug-and-Playcited by 108
  9. 2018Adversarial Regularizers in Inverse Problemscited by 103
  10. 2018Regularization by Denoising: Clarifications and New Interpretationscited by 103
  11. 2022Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imagingcited by 96
  12. 2018NETT: Solving Inverse Problems with Deep Neural Networkscited by 89
10 more
  1. 2022Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularizationcited by 80
  2. 2020Learned convex regularizers for inverse problemscited by 55
  3. 2020Total Deep Variation for Linear Inverse Problemscited by 53
  4. 2022Learned reconstruction methods with convergence guaranteescited by 46
  5. 2018Subgradient methods for sharp weakly convex functionscited by 33
  6. 2021End-to-end reconstruction meets data-driven regularization for inverse problemscited by 32
  7. 2023Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithmscited by 31
  8. 2020Nonconvex regularization for sparse neural networkscited by 7
  9. 2022Optimal Regularization for a Data Sourcecited by 6
  10. 2023Convex Latent-Optimized Adversarial Regularizers for Imaging Inverse Problemscited by 2

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Cited by year

Citing papers per year: 2024: 3; 2025: 1.

4 papers.

  1. 2024Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groupscited by 24
  2. 2025Learning Regularization Functionals for Inverse Problems: A Comparative Studycited by 15
  3. 2024Weakly Convex Regularisers for Inverse Problems: Convergence of Critical Points and Primal-Dual Optimisationcited by 14
  4. 2024Unsupervised Training of Convex Regularizers using Maximum Likelihood Estimationcited by 3