mlsanityData to 14 Oct 2026

Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms

arXiv 2308.10542 ↗First posted 21 Aug 2023eess.IV cs.CV cs.LGcited by 31

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Abstract (arXiv)

We propose to learn non-convex regularizers with a prescribed upper bound on their weak-convexity modulus. Such regularizers give rise to variational denoisers that minimize a convex energy. They rely on few parameters (less than 15,000) and offer a signal-processing interpretation as they mimic handcrafted sparsity-promoting regularizers. Through numerical experiments, we show that such denoisers outperform convex-regularization methods as well as the popular BM3D denoiser. Additionally, the learned regularizer can be deployed to solve inverse problems with iterative schemes that provably converge. For both CT and MRI reconstruction, the regularizer generalizes well and offers an excellent tradeoff between performance, number of parameters, guarantees, and interpretability when compared to other data-driven approaches.

Key facts. Cited by 31 papers in the map (data through 14 Oct 2026). Builds on 24 of its 58 references that are in the map. First posted on arXiv 21 Aug 2023.

Builds on

24 of 58 references.

References · 24

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2019Deep Equilibrium Modelscited by 615
  3. 2020Plug-and-Play Image Restoration with Deep Denoiser Priorcited by 470
  4. 2015Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restorationcited by 195
  5. 2021Gradient Step Denoiser for convergent Plug-and-Playcited by 108
  6. 2018Adversarial Regularizers in Inverse Problemscited by 103
  7. 2018The Singular Values of Convolutional Layerscited by 95
  8. 2018NETT: Solving Inverse Problems with Deep Neural Networkscited by 89
  9. 2022Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularizationcited by 80
  10. 2013Accelerated Gradient Methods for Nonconvex Nonlinear and Stochastic Programmingcited by 75
  11. 2020Learned convex regularizers for inverse problemscited by 55
  12. 2020Total Deep Variation for Linear Inverse Problemscited by 53
12 more
  1. 2022Learned reconstruction methods with convergence guaranteescited by 46
  2. 2022A Neural-Network-Based Convex Regularizer for Inverse Problemscited by 41
  3. 2018A characterization of proximity operatorscited by 32
  4. 2014iPiano: Inertial Proximal Algorithm for Non-Convex Optimizationcited by 30
  5. 2022Improving Lipschitz-Constrained Neural Networks by Learning Activation Functionscited by 24
  6. 2014Insights into analysis operator learning: From patch-based sparse models to higher-order MRFscited by 18
  7. 2022Approximation of Lipschitz Functions using Deep Spline Neural Networkscited by 15
  8. 2023A relaxed proximal gradient descent algorithm for convergent plug-and-play with proximal denoisercited by 12
  9. 2016Local Convergence of the Heavy-ball Method and iPiano for Non-convex Optimizationcited by 9
  10. 2021Learning convex regularizers satisfying the variational source condition for inverse problemscited by 8
  11. 2019Linearly Involved Generalized Moreau Enhanced Models and Their Proximal Splitting Algorithm under Overall Convexity Conditioncited by 5
  12. 2015Convex Denoising using Non-Convex Tight Frame Regularizationcited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 8; 2025: 12; 2026: 9.

31 papers.

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  1. 2025Flower: A Flow-Matching Solver for Inverse Problemscited by 27
  2. 2023What's in a Prior? Learned Proximal Networks for Inverse Problemscited by 25
  3. 2025Learning Regularization Functionals for Inverse Problems: A Comparative Studycited by 15
  4. 2024Weakly Convex Regularisers for Inverse Problems: Convergence of Critical Points and Primal-Dual Optimisationcited by 14
  5. 2025DEALing with Image Reconstruction: Deep Attentive Least Squarescited by 6
  6. 2024Stability of Data-Dependent Ridge-Regularization for Inverse Problemscited by 5
  7. 2023Provably Convergent Data-Driven Convex-Nonconvex Regularizationcited by 4
  8. 2024Iteratively Refined Image Reconstruction with Learned Attentive Regularizerscited by 3
  9. 2024The Star Geometry of Critic-Based Regularizer Learningcited by 3
  10. 2024A primal-dual algorithm for image reconstruction with input-convex neural network regularizerscited by 3
  11. 2024You KAN Do It in a Single Shot: Plug-and-Play Methods with Single-Instance Priorscited by 2
  12. 2025Efficient Bayesian Computation Using Plug-and-Play Priors for Poisson Inverse Problemscited by 2
19 more
  1. 2025Multivariate Fields of Experts for Convergent Image Reconstructioncited by 2
  2. 2025Nonasymptotic Convergence Rates for Plug-and-Play Methods With MMSE Denoiserscited by 2
  3. 2026A Stability Benchmark of Generative Regularizers for Inverse Problemscited by 2
  4. 2024Controlled Learning of Pointwise Nonlinearities in Neural-Network-Like Architecturescited by 1
  5. 2025Universal Architectures for the Learning of Polyhedral Norms and Convex Regularizerscited by 1
  6. 2025VibrantLeaves: A principled parametric image generator for training deep restoration modelscited by 1
  7. 2025Learning Binary Sampling Patterns for Single-Pixel Imaging using Bilevel Optimisationcited by 1
  8. 2026Weakly Convex Ridge Regularization for 3D Non-Cartesian MRI Reconstructioncited by 1
  9. 2024Gradient Networkscited by 0
  10. 2025MAP Image Recovery with Guarantees using Locally Convex Multi-Scale Energy (LC-MUSE) Modelcited by 0
  11. 2025Breaking the Weak Recovery Limit in Random Phase Retrieval with Learned Regularizerscited by 0
  12. 2025Bilevel Learning via Inexact Stochastic Gradient Descentcited by 0
  13. 2026Latent Space Inference via Paired Autoencoderscited by 0
  14. 2026Learned Finite Element-based Regularization of the Inverse Problem in Electrocardiographic Imagingcited by 0
  15. 2026Semantic Segmentation for Histopathology using Learned Regularization based on Global Proportionscited by 0
  16. 2026Stabilizing Deep Reconstruction Operators with Contractive Anchoringcited by 0
  17. 2026Trainable Nonexpansive Denoisers for Contractive Image Reconstructioncited by 0
  18. 2026CLEAR: Complex Learned Explicit Analytical Regularization for Ultra-Accelerated 4D Flow CMR Reconstructioncited by 0
  19. 2026Taming Nonconvexity with Epigraph Liftingcited by 0