mlsanityData to 14 Oct 2026

Learned reconstruction methods with convergence guarantees

arXiv 2206.05431 ↗First posted 11 Jun 2022cs.CV cs.LGcited by 46

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Abstract (arXiv)

In recent years, deep learning has achieved remarkable empirical success for image reconstruction. This has catalyzed an ongoing quest for precise characterization of correctness and reliability of data-driven methods in critical use-cases, for instance in medical imaging. Notwithstanding the excellent performance and efficacy of deep learning-based methods, concerns have been raised regarding their stability, or lack thereof, with serious practical implications. Significant advances have been made in recent years to unravel the inner workings of data-driven image recovery methods, challenging their widely perceived black-box nature. In this article, we will specify relevant notions of convergence for data-driven image reconstruction, which will form the basis of a survey of learned methods with mathematically rigorous reconstruction guarantees. An example that is highlighted is the role of ICNN, offering the possibility to combine the power of deep learning with classical convex regularization theory for devising methods that are provably convergent. This survey article is aimed at both methodological researchers seeking to advance the frontiers of our understanding of data-driven image reconstruction methods as well as practitioners, by providing an accessible description of useful convergence concepts and by placing some of the existing empirical practices on a solid mathematical foundation.

Key facts. Cited by 46 papers in the map (data through 14 Oct 2026). Builds on 37 of its 64 references that are in the map. First posted on arXiv 11 Jun 2022.

Builds on

37 of 64 references.

References · 37

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  3. 2016Deep Convolutional Neural Network for Inverse Problems in Imagingcited by 433
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25 more
  1. 2018Adversarial Regularizers in Inverse Problemscited by 103
  2. 2018Regularization by Denoising: Clarifications and New Interpretationscited by 103
  3. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 97
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  6. 2015Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolationcited by 78
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  8. 2018Deep Bayesian Inversioncited by 61
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 15; 2024: 13; 2025: 12; 2026: 6.

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  1. 2023Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithmscited by 31
  2. 2023Equivariant Bootstrapping for Uncertainty Quantification in Imaging Inverse Problemscited by 17
  3. 2023Provably Convergent Plug-and-Play Quasi-Newton Methodscited by 15
  4. 2025Learning Regularization Functionals for Inverse Problems: A Comparative Studycited by 15
  5. 2024Weakly Convex Regularisers for Inverse Problems: Convergence of Critical Points and Primal-Dual Optimisationcited by 14
  6. 2023Convergent regularization in inverse problems and linear plug-and-play denoiserscited by 13
  7. 2023Learning from small data sets: Patch-based regularizers in inverse problems for image reconstructioncited by 9
  8. 2023The Perception-Robustness Tradeoff in Deterministic Image Restorationcited by 7
  9. 2023Model-corrected learned primal-dual models for fast limited-view photoacoustic tomographycited by 6
  10. 2024Do Bayesian imaging methods report trustworthy probabilities?cited by 6
  11. 2025Learning few-step posterior samplers by unfolding and distillation of diffusion modelscited by 6
  12. 2024Stability of Data-Dependent Ridge-Regularization for Inverse Problemscited by 5
34 more
  1. 2025Good Things Come in Pairs: Paired Autoencoders for Inverse Problemscited by 5
  2. 2023Provably Convergent Data-Driven Convex-Nonconvex Regularizationcited by 4
  3. 2023Unsupervised approaches based on optimal transport and convex analysis for inverse problems in imagingcited by 4
  4. 2023Inverse Problems with Learned Forward Operatorscited by 4
  5. 2023Convergence and Recovery Guarantees of Unsupervised Neural Networks for Inverse Problemscited by 3
  6. 2024Unsupervised Training of Convex Regularizers using Maximum Likelihood Estimationcited by 3
  7. 2024Bayesian computation with generative diffusion models by Multilevel Monte Carlocited by 3
  8. 2023Convergence Guarantees of Overparametrized Wide Deep Inverse Priorcited by 2
  9. 2023Learned Regularization for Inverse Problems: Insights from a Spectral Modelcited by 2
  10. 2024Invertible ResNets for Inverse Imaging Problems: Competitive Performance with Provable Regularization Propertiescited by 2
  11. 2025Efficient Bayesian Computation Using Plug-and-Play Priors for Poisson Inverse Problemscited by 2
  12. 2025Prompting Lipschitz-constrained network for multiple-in-one sparse-view CT reconstructioncited by 2
  13. 2026Error Analysis of Bayesian Inverse Problems with Generative Priorscited by 2
  14. 2023Learned reconstruction methods for inverse problems: sample error estimatescited by 1
  15. 2024Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overviewcited by 1
  16. 2024Robust width: A lightweight and certifiable adversarial defensecited by 1
  17. 2025Universal Architectures for the Learning of Polyhedral Norms and Convex Regularizerscited by 1
  18. 2025Graph Neural Regularizers for PDE Inverse Problemscited by 1
  19. 2026Efficient Unrolled Networks for Large-Scale 3D Inverse Problemscited by 1
  20. 2026Learning spatially adaptive sparsity level maps for arbitrary convolutional dictionariescited by 1
  21. 2023Meta-Prior: Meta learning for Adaptive Inverse Problem Solverscited by 0
  22. 2024R2D2 image reconstruction with model uncertainty quantification in radio astronomycited by 0
  23. 2024Maximum Discrepancy Generative Regularization and Non-Negative Matrix Factorization for Single Channel Source Separationcited by 0
  24. 2024Continuous Learned Primal Dualcited by 0
  25. 2024LAMA: Stable Dual-Domain Deep Reconstruction For Sparse-View CTcited by 0
  26. 2024The learned range test method for the inverse inclusion problemcited by 0
  27. 2025Tuning-Free Structured Sparse PCA via Deep Unfolding Networkscited by 0
  28. 2025Hypothesis Testing in Imaging Inverse Problemscited by 0
  29. 2025Deep Unfolding Network for Nonlinear Multi-Frequency Electrical Impedance Tomographycited by 0
  30. 2025LAMA-Net: A Convergent Network Architecture for Dual-Domain Reconstructioncited by 0
  31. 2025Bayesian model selection and misspecification testing in imaging inverse problems only from noisy and partial measurementscited by 0
  32. 2026Deep unfolding of MCMC kernels: scalable, modular & explainable GANs for high-dimensional posterior samplingcited by 0
  33. 2026A Distributionally Robust Framework for Learned Reconstructions in Inverse Problemscited by 0
  34. 2026Learning spatially varying regularisation parameters of low regularity for image reconstructioncited by 0