mlsanityData to 13 Oct 2026

Feasibility-based Fixed Point Networks

arXiv 2104.14090 ↗First posted 29 Apr 2021cs.LGcited by 17

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Abstract (arXiv)

Inverse problems consist of recovering a signal from a collection of noisy measurements. These problems can often be cast as feasibility problems; however, additional regularization is typically necessary to ensure accurate and stable recovery with respect to data perturbations. Hand-chosen analytic regularization can yield desirable theoretical guarantees, but such approaches have limited effectiveness recovering signals due to their inability to leverage large amounts of available data. To this end, this work fuses data-driven regularization and convex feasibility in a theoretically sound manner. This is accomplished using feasibility-based fixed point networks (F-FPNs). Each F-FPN defines a collection of nonexpansive operators, each of which is the composition of a projection-based operator and a data-driven regularization operator. Fixed point iteration is used to compute fixed points of these operators, and weights of the operators are tuned so that the fixed points closely represent available data. Numerical examples demonstrate performance increases by F-FPNs when compared to standard TV-based recovery methods for CT reconstruction and a comparable neural network based on algorithm unrolling.

Key facts. Cited by 17 papers in the map (data through 13 Oct 2026). Builds on 45 of its 122 references that are in the map. First posted on arXiv 29 Apr 2021.

Builds on

45 of 122 references.

References · 45

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,950
  2. 2014Adam: A Method for Stochastic Optimizationcited by 37,093
  3. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,223
  4. 2018Neural Ordinary Differential Equationscited by 3,750
  5. 2016Optimization Methods for Large-Scale Machine Learningcited by 1,142
  6. 2019Deep Equilibrium Modelscited by 606
  7. 2016Deep Convolutional Neural Network for Inverse Problems in Imagingcited by 432
  8. 2019Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processingcited by 416
  9. 2017Learning Deep CNN Denoiser Prior for Image Restorationcited by 408
  10. 2017Stable Architectures for Deep Neural Networkscited by 340
  11. 2017Learned Primal-dual Reconstructioncited by 251
  12. 2016Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applicationscited by 245
33 more
  1. 2021Learning to Optimize: A Primer and A Benchmarkcited by 206
  2. 2015Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restorationcited by 195
  3. 2020Multiscale Deep Equilibrium Modelscited by 150
  4. 2017Solving ill-posed inverse problems using iterative deep neural networkscited by 145
  5. 2019Deep Plug-and-Play Super-Resolution for Arbitrary Blur Kernelscited by 112
  6. 2017Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problemscited by 107
  7. 2018Adversarial Regularizers in Inverse Problemscited by 102
  8. 2020Monotone operator equilibrium networkscited by 100
  9. 2018Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholdscited by 84
  10. 2017One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Modelscited by 67
  11. 2017Learned D-AMP: Principled Neural Network based Compressive Image Recoverycited by 65
  12. 2020Regularization by Denoising via Fixed-Point Projection (RED-PRO)cited by 55
  13. 2020Learned convex regularizers for inverse problemscited by 55
  14. 2018Neural Proximal Gradient Descent for Compressive Imagingcited by 46
  15. 2017Unrolled Optimization with Deep Priorscited by 40
  16. 2017Recurrent Inference Machines for Solving Inverse Problemscited by 33
  17. 2013A computational framework for infinite-dimensional Bayesian inverse problems. Part I: The linearized case, with application to global seismic inversioncited by 32
  18. 2018Universal Approximation with Quadratic Deep Networkscited by 29
  19. 2017Learned Convolutional Sparse Codingcited by 26
  20. 2019Differentiable Linearized ADMMcited by 18
  21. 2019Controlling Neural Networks via Energy Dissipationcited by 12
  22. 2019The LoDoPaB-CT Dataset: A Benchmark Dataset for Low-Dose CT Reconstruction Methodscited by 12
  23. 2018A two-stage method for spectral-spatial classification of hyperspectral imagescited by 5
  24. 2013Projection Methods: Swiss Army Knives for Solving Feasibility and Best Approximation Problems with Halfspacescited by 4
  25. 2014A sparse Kaczmarz solver and a linearized Bregman method for online compressed sensingcited by 4
  26. 2016Linear convergence of the Randomized Sparse Kaczmarz Methodcited by 4
  27. 2019Degrees of Freedom Analysis of Unrolled Neural Networkscited by 4
  28. 2018Multigrid Optimization for Large-Scale Ptychographic Phase Retrievalcited by 3
  29. 2014Projection Methods: An Annotated Bibliography of Books and Reviewscited by 2
  30. 2018Asynchronous Sequential Inertial Iterations for Common Fixed Points Problems with an Application to Linear Systemscited by 2
  31. 2014Weak and Strong Superiorization: Between Feasibility-Seeking and Minimizationcited by 1
  32. 2015Superiorization and Perturbation Resilience of Algorithms: A Continuously Updated Bibliographycited by 1
  33. 2017A Real-time Image Reconstruction System for Particle Treatment Planning Using Proton Computed Tomography (pCT)cited by 1

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2021: 4; 2022: 3; 2023: 2; 2024: 3; 2025: 3; 2026: 2.

17 papers.

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  1. 2021SHINE: SHaring the INverse Estimate from the forward pass for bi-level optimization and implicit modelscited by 26
  2. 2022Explainable AI via Learning to Optimizecited by 14
  3. 2022Near-Exact Recovery for Tomographic Inverse Problems via Deep Learningcited by 13
  4. 2024On Logical Extrapolation for Mazes with Recurrent and Implicit Networkscited by 7
  5. 2021Equilibrated Zeroth-Order Unrolled Deep Networks for Accelerated MRIcited by 5
  6. 2024A Generalization Bound for a Family of Implicit Networkscited by 4
  7. 2025End-to-End Training of High-Dimensional Optimal Control with Implicit Hamiltonians via Jacobian-Free Backpropagationcited by 3
  8. 2022Hybrid Far- and Near-Field Channel Estimation for THz Ultra-Massive MIMO via Fixed Point Networkscited by 2
  9. 2023Efficient Model-Based Deep Learning via Network Pruning and Fine-Tuningcited by 2
  10. 2021Supervised learning of analysis-sparsity priors with automatic differentiationcited by 1
  11. 2026On the Convergence of Jacobian-Free Backpropagation for Optimal Control Problems with Implicit Hamiltonianscited by 1
  12. 2021Operator Splitting for Learning to Predict Equilibria in Convex Gamescited by 0
5 more
  1. 2023CQnet: convex-geometric interpretation and constraining neural-network trajectoriescited by 0
  2. 2024Training Implicit Networks for Image Deblurring using Jacobian-Free Backpropagationcited by 0
  3. 2025Deep Recurrence for Dynamical Segmentation Modelscited by 0
  4. 2025Deep Feedback Modelscited by 0
  5. 2026End-to-End Learning of Safe Optimal Feedback Control in High Dimensions with Control Barrier Function Layerscited by 0