mlsanityData to 14 Oct 2026

Adversarial Regularizers in Inverse Problems

arXiv 1805.11572 ↗First posted 29 May 2018cs.CV cs.LG cs.NAcited by 103

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Abstract (arXiv)

Inverse Problems in medical imaging and computer vision are traditionally solved using purely model-based methods. Among those variational regularization models are one of the most popular approaches. We propose a new framework for applying data-driven approaches to inverse problems, using a neural network as a regularization functional. The network learns to discriminate between the distribution of ground truth images and the distribution of unregularized reconstructions. Once trained, the network is applied to the inverse problem by solving the corresponding variational problem. Unlike other data-based approaches for inverse problems, the algorithm can be applied even if only unsupervised training data is available. Experiments demonstrate the potential of the framework for denoising on the BSDS dataset and for computed tomography reconstruction on the LIDC dataset.

Key facts. Cited by 103 papers in the map (data through 14 Oct 2026). First posted on arXiv 29 May 2018.

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Citing papers per year: 2021: 23; 2022: 10; 2023: 25; 2024: 20; 2025: 11; 2026: 14.

103 papers.

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  1. 2021Learning to Optimize: A Primer and A Benchmarkcited by 208
  2. 2021Gradient Step Denoiser for convergent Plug-and-Playcited by 108
  3. 2022Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularizationcited by 80
  4. 2022Learned reconstruction methods with convergence guaranteescited by 46
  5. 2022A Neural-Network-Based Convex Regularizer for Inverse Problemscited by 41
  6. 2021Wasserstein GANs Work Because They Fail (to Approximate the Wasserstein Distance)cited by 35
  7. 2021End-to-end reconstruction meets data-driven regularization for inverse problemscited by 32
  8. 2023Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithmscited by 31
  9. 2021Equivariant neural networks for inverse problemscited by 29
  10. 2021Learning the optimal Tikhonov regularizer for inverse problemscited by 26
  11. 2023What's in a Prior? Learned Proximal Networks for Inverse Problemscited by 25
  12. 2021Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks: Theory, Methods, and Algorithmscited by 24
38 more
  1. 2024Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groupscited by 24
  2. 2021Generalized Normalizing Flows via Markov Chainscited by 23
  3. 2021Regularising Inverse Problems with Generative Machine Learning Modelscited by 22
  4. 2022PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularizationcited by 22
  5. 2021Feasibility-based Fixed Point Networkscited by 17
  6. 2023Manifold Learning by Mixture Models of VAEs for Inverse Problemscited by 17
  7. 2023Variational Bayesian Imaging with an Efficient Surrogate Score-based Priorcited by 17
  8. 2024Plug-and-Play image restoration with Stochastic deNOising REgularizationcited by 17
  9. 2021Learning local regularization for variational image restorationcited by 16
  10. 2023Provably Convergent Plug-and-Play Quasi-Newton Methodscited by 15
  11. 2025Learning Regularization Functionals for Inverse Problems: A Comparative Studycited by 15
  12. 2024Weakly Convex Regularisers for Inverse Problems: Convergence of Critical Points and Primal-Dual Optimisationcited by 14
  13. 2023Convergent regularization in inverse problems and linear plug-and-play denoiserscited by 13
  14. 2021TNet: A Model-Constrained Tikhonov Network Approach for Inverse Problemscited by 10
  15. 2023Learning from small data sets: Patch-based regularizers in inverse problems for image reconstructioncited by 9
  16. 2021Learning convex regularizers satisfying the variational source condition for inverse problemscited by 8
  17. 2021Inverse Aerodynamic Design of Gas Turbine Blades using Probabilistic Machine Learningcited by 7
  18. 2023Learning Gradients of Convex Functions with Monotone Gradient Networkscited by 7
  19. 2025Approximation theory for 1-Lipschitz ResNetscited by 7
  20. 2021Wasserstein GANs with Gradient Penalty Compute Congested Transportcited by 6
  21. 2022Optimal Regularization for a Data Sourcecited by 6
  22. 2023Restoration based Generative Modelscited by 6
  23. 2024QN-Mixer: A Quasi-Newton MLP-Mixer Model for Sparse-View CT Reconstructioncited by 6
  24. 2025DEALing with Image Reconstruction: Deep Attentive Least Squarescited by 6
  25. 2021Adversarially learned iterative reconstruction for imaging inverse problemscited by 5
  26. 2022Deep unfolding as iterative regularization for imaging inverse problemscited by 5
  27. 2023Solving Low-Dose CT Reconstruction via GAN with Local Coherencecited by 5
  28. 2024Stability of Data-Dependent Ridge-Regularization for Inverse Problemscited by 5
  29. 2024Particle-Filtering-based Latent Diffusion for Inverse Problemscited by 5
  30. 2025Good Things Come in Pairs: Paired Autoencoders for Inverse Problemscited by 5
  31. 2023NF-ULA: Langevin Monte Carlo with Normalizing Flow Prior for Imaging Inverse Problemscited by 4
  32. 2023Provably Convergent Data-Driven Convex-Nonconvex Regularizationcited by 4
  33. 2023Unsupervised approaches based on optimal transport and convex analysis for inverse problems in imagingcited by 4
  34. 2024Differentiable programming across the PDE and Machine Learning barriercited by 4
  35. 2021Convergence and finite sample approximations of entropic regularized Wasserstein distances in Gaussian and RKHS settingscited by 3
  36. 2021Designing Rotationally Invariant Neural Networks from PDEs and Variational Methodscited by 3
  37. 2024Learning a Gaussian Mixture for Sparsity Regularization in Inverse Problemscited by 3
  38. 2024Unsupervised Training of Convex Regularizers using Maximum Likelihood Estimationcited by 3

50 most cited of 103 All 103 (JSON)