mlsanityData to 14 Oct 2026

Equivariant plug-and-play image reconstruction

arXiv 2312.01831 ↗First posted 4 Dec 2023eess.IV cs.CVcited by 26

Not on the map. Why?

Abstract (arXiv)

Plug-and-play algorithms constitute a popular framework for solving inverse imaging problems that rely on the implicit definition of an image prior via a denoiser. These algorithms can leverage powerful pre-trained denoisers to solve a wide range of imaging tasks, circumventing the necessity to train models on a per-task basis. Unfortunately, plug-and-play methods often show unstable behaviors, hampering their promise of versatility and leading to suboptimal quality of reconstructed images. In this work, we show that enforcing equivariance to certain groups of transformations (rotations, reflections, and/or translations) on the denoiser strongly improves the stability of the algorithm as well as its reconstruction quality. We provide a theoretical analysis that illustrates the role of equivariance on better performance and stability. We present a simple algorithm that enforces equivariance on any existing denoiser by simply applying a random transformation to the input of the denoiser and the inverse transformation to the output at each iteration of the algorithm. Experiments on multiple imaging modalities and denoising networks show that the equivariant plug-and-play algorithm improves both the reconstruction performance and the stability compared to their non-equivariant counterparts.

Key facts. Cited by 26 papers in the map (data through 14 Oct 2026). Builds on 39 of its 54 references that are in the map. First posted on arXiv 4 Dec 2023.

Builds on

39 of 54 references.

References · 39

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2021SwinIR: Image Restoration Using Swin Transformercited by 1,887
  3. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,416
  4. 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,358
  5. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  6. 2016Group Equivariant Convolutional Networkscited by 1,165
  7. 2022Denoising Diffusion Restoration Modelscited by 963
  8. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 607
  9. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 602
  10. 2018fastMRI: An Open Dataset and Benchmarks for Accelerated MRIcited by 470
  11. 2020Plug-and-Play Image Restoration with Deep Denoiser Priorcited by 470
  12. 2019General E(2)-Equivariant Steerable CNNscited by 446
27 more
  1. 2016Deep Convolutional Neural Network for Inverse Problems in Imagingcited by 433
  2. 2023Denoising Diffusion Models for Plug-and-Play Image Restorationcited by 340
  3. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 307
  4. 2019Plug-and-Play Methods Provably Converge with Properly Trained Denoiserscited by 198
  5. 2021Gradient Step Denoiser for convergent Plug-and-Playcited by 108
  6. 2017Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problemscited by 107
  7. 2018Regularization by Denoising: Clarifications and New Interpretationscited by 103
  8. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 97
  9. 2022Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imagingcited by 96
  10. 2021Equivariant Imaging: Learning Beyond the Range Spacecited by 83
  11. 2019Plug and play methods for magnetic resonance imaging (long version)cited by 75
  12. 2017One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Modelscited by 67
  13. 2020Learning Maximally Monotone Operators for Image Recoverycited by 62
  14. 2021Equivariant Q Learning in Spatial Action Spacescited by 62
  15. 2020Regularization by Denoising via Fixed-Point Projection (RED-PRO)cited by 55
  16. 2015Seven ways to improve example-based single image super resolutioncited by 51
  17. 2021Recovery of Continuous 3D Refractive Index Maps from Discrete Intensity-Only Measurements using Neural Fieldscited by 48
  18. 2022Imaging with Equivariant Deep Learningcited by 35
  19. 2021Equivariant neural networks for inverse problemscited by 29
  20. 2022Sensing Theorems for Unsupervised Learning in Linear Inverse Problemscited by 28
  21. 2021Rotation-Equivariant Deep Learning for Diffusion MRIcited by 20
  22. 20234D Panoptic Segmentation as Invariant and Equivariant Field Predictioncited by 19
  23. 2021Equivariant Wavelets: Fast Rotation and Translation Invariant Wavelet Scattering Transformscited by 6
  24. 2022Deep invariant networks with differentiable augmentation layerscited by 6
  25. 2014A forward-backward view of some primal-dual optimization methods in image recoverycited by 5
  26. 2023Convergent plug-and-play with proximal denoiser and unconstrained regularization parametercited by 5
  27. 2023Fluctuation-based deconvolution in fluorescence microscopy using plug-and-play denoiserscited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 7; 2025: 13; 2026: 6.

26 papers.

Sort:

By area:

  1. 2024Analysis of Deep Image Prior and Exploiting Self-Guidance for Image Reconstructioncited by 11
  2. 2024Constrained Diffusion with Trust Samplingcited by 10
  3. 2025MRI Super-Resolution with Deep Learning: A Comprehensive Surveycited by 7
  4. 2024Empirical Bayesian image restoration by Langevin sampling with a denoising diffusion implicit priorcited by 6
  5. 2025Good Things Come in Pairs: Paired Autoencoders for Inverse Problemscited by 5
  6. 2025Rotation Equivariant Arbitrary-scale Image Super-Resolutioncited by 5
  7. 2025NPN: Non-Linear Projections of the Null-Space for Imaging Inverse Problemscited by 4
  8. 2025EquiReg: Equivariance Regularized Diffusion for Inverse Problemscited by 3
  9. 2024From Learning to Optimize to Learning Optimization Algorithmscited by 2
  10. 2024Robust plug-and-play methods for highly accelerated non-Cartesian MRI reconstructioncited by 2
  11. 2024A Tunable Despeckling Neural Network Stabilized via Diffusion Equationcited by 2
  12. 2025Reconstruct Anything Model: a lightweight general model for computational imagingcited by 2
14 more
  1. 2025Efficient Bayesian Computation Using Plug-and-Play Priors for Poisson Inverse Problemscited by 2
  2. 2025Axis-level Symmetry Detection with Group-Equivariant Representationcited by 2
  3. 2026An analytic theory of convolutional neural network inverse problems solverscited by 2
  4. 2024Equivariant Denoisers for Image Restorationcited by 1
  5. 2025Equivariant Splitting: Self-supervised learning from incomplete datacited by 1
  6. 2025Equivariant Sampling for Improving Diffusion Model-based Image Restorationcited by 1
  7. 2026GSNR: Graph Smooth Null-Space Representation for Inverse Problemscited by 1
  8. 2025Fast Equivariant Imaging: Accelerating Unsupervised Learning and Model Adaptation via Inexact Splittingcited by 0
  9. 2025prNet: Data-Driven Phase Retrieval via Stochastic Refinementcited by 0
  10. 2025Bregman geometry-aware split Gibbs sampling for Bayesian Poisson inverse problemscited by 0
  11. 2026Multilevel Stochastic Plug-and-Play for Sparse-View CT Reconstructioncited by 0
  12. 2026Stabilizing Deep Reconstruction Operators with Contractive Anchoringcited by 0
  13. 2026Embedding Rotation Invariance for Provable Multi-Oriented Scene Text Recognitioncited by 0
  14. 2026Convergent Plug-and-Play Image Restoration with Annealed Noise Levelscited by 0