mlsanityData to 7 Oct 2026

Imaging with Equivariant Deep Learning

arXiv 2209.01725 ↗First posted 5 Sep 2022eess.SP cs.CVcited by 35

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Abstract (arXiv)

From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refers to the invariance property of signal sets to transformations such as translation, rotation or scaling. Symmetry can also be incorporated into deep neural networks in the form of equivariance, allowing for more data-efficient learning. While there has been important advances in the design of end-to-end equivariant networks for image classification in recent years, computational imaging introduces unique challenges for equivariant network solutions since we typically only observe the image through some noisy ill-conditioned forward operator that itself may not be equivariant. We review the emerging field of equivariant imaging and show how it can provide improved generalization and new imaging opportunities. Along the way we show the interplay between the acquisition physics and group actions and links to iterative reconstruction, blind compressed sensing and self-supervised learning.

Key facts. Cited by 35 papers in the map (data through 7 Oct 2026). Builds on 25 of its 42 references that are in the map. First posted on arXiv 5 Sep 2022.

Builds on

25 of 42 references.

References · 25

  1. 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,352
  2. 2016Group Equivariant Convolutional Networkscited by 1,154
  3. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  4. 2019General E(2)-Equivariant Steerable CNNscited by 441
  5. 2016Deep Convolutional Neural Network for Inverse Problems in Imagingcited by 431
  6. 2019Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processingcited by 411
  7. 2017Compressed Sensing using Generative Modelscited by 337
  8. 2020Deep Learning Techniques for Inverse Problems in Imagingcited by 290
  9. 2014Understanding image representations by measuring their equivariance and equivalencecited by 240
  10. 2020End-to-End Variational Networks for Accelerated MRI Reconstructioncited by 201
  11. 2019Robust and interpretable blind image denoising via bias-free convolutional neural networkscited by 87
  12. 2021Equivariant Imaging: Learning Beyond the Range Spacecited by 83
13 more
  1. 2019Plug and play methods for magnetic resonance imaging (long version)cited by 75
  2. 2021Coordinate Independent Convolutional Networks -- Isometry and Gauge Equivariant Convolutions on Riemannian Manifoldscited by 72
  3. 2019RARE: Image Reconstruction using Deep Priors Learned without Ground Truthcited by 64
  4. 2019Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learningcited by 60
  5. 2021Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurementscited by 56
  6. 2018Deep Residual Learning for Accelerated MRI using Magnitude and Phase Networkscited by 53
  7. 2019Improved Generalization Bounds of Group Invariant / Equivariant Deep Networks via Quotient Feature Spacescited by 34
  8. 2021Equivariant neural networks for inverse problemscited by 29
  9. 2022Sensing Theorems for Unsupervised Learning in Linear Inverse Problemscited by 28
  10. 2021Data augmentation for deep learning based accelerated MRI reconstruction with limited datacited by 19
  11. 2021Truly shift-equivariant convolutional neural networks with adaptive polyphase upsamplingcited by 10
  12. 2015FRIST - Flipping and Rotation Invariant Sparsifying Transform Learning and Applicationscited by 7
  13. 2020Performance characterization of a novel deep learning-based MR image reconstruction pipelinecited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 8; 2024: 9; 2025: 8; 2026: 10.

35 papers.

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  1. 2023Equivariant Multi-Modality Image Fusioncited by 98
  2. 2023Equivariant Adaptation of Large Pretrained Modelscited by 40
  3. 2023Equivariant plug-and-play image reconstructioncited by 26
  4. 2023What's in a Prior? Learned Proximal Networks for Inverse Problemscited by 24
  5. 2024Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groupscited by 23
  6. 2023Equivariant Bootstrapping for Uncertainty Quantification in Imaging Inverse Problemscited by 17
  7. 2024Diffusion Posterior Proximal Sampling for Image Restorationcited by 14
  8. 2023Fully Convolutional Slice-to-Volume Reconstruction for Single-Stack MRIcited by 10
  9. 2023Self-Supervised Scalable Deep Compressed Sensingcited by 8
  10. 2024Improved Canonicalization for Model Agnostic Equivariancecited by 7
  11. 2025MRI Super-Resolution with Deep Learning: A Comprehensive Surveycited by 7
  12. 2024Do Bayesian imaging methods report trustworthy probabilities?cited by 6
23 more
  1. 2024Perspective-Equivariance for Unsupervised Imaging with Camera Geometrycited by 5
  2. 2024Equivariant Imaging for Self-supervised Hyperspectral Image Inpaintingcited by 5
  3. 2025Benchmarking Self-Supervised Learning Methods for Accelerated MRI Reconstructioncited by 4
  4. 2024WaveMo: Learning Wavefront Modulations to See Through Scatteringcited by 3
  5. 2024SRE-CNN: A Spatiotemporal Rotation-Equivariant CNN for Cardiac Cine MR Imagingcited by 3
  6. 2023Convergence analysis of equilibrium methods for inverse problemscited by 2
  7. 2024From Learning to Optimize to Learning Optimization Algorithmscited by 2
  8. 2026An analytic theory of convolutional neural network inverse problems solverscited by 2
  9. 2025Bi-directional Self-Registration for Misaligned Infrared-Visible Image Fusioncited by 1
  10. 2025EquiReg: Equivariance Regularized Diffusion for Inverse Problemscited by 1
  11. 2025Equivariant Sampling for Improving Diffusion Model-based Image Restorationcited by 1
  12. 2026SHARE: A Fully Unsupervised Framework for Single Hyperspectral Image Restorationcited by 1
  13. 2026Riemannian AmbientFlow: Towards Simultaneous Manifold Learning and Generative Modeling from Corrupted Datacited by 1
  14. 2026PolarAPP: Beyond Polarization Demosaicking for Polarimetric Applicationscited by 1
  15. 2025Hypothesis Testing in Imaging Inverse Problemscited by 0
  16. 2025DUN-SRE: Deep Unrolling Network with Spatiotemporal Rotation Equivariance for Dynamic MRI Reconstructioncited by 0
  17. 2025Bayesian model selection and misspecification testing in imaging inverse problems only from noisy and partial measurementscited by 0
  18. 2026Deep Lightweight Unrolled Network for High Dynamic Range Modulo Imagingcited by 0
  19. 2026Equivariant Learning for Unsupervised Image Dehazingcited by 0
  20. 2026Scale Equivariance Regularization and Feature Lifting in High Dynamic Range Modulo Imagingcited by 0
  21. 2026UNet-AF: Alias-free UNet architecturescited by 0
  22. 2026Target localization, identification and sensing using latent symmetriescited by 0
  23. 2026PE-CSNet: An equivariant network architecture with learnable patch-based sparse representationcited by 0