mlsanityData to 7 Oct 2026

Equivariant Imaging: Learning Beyond the Range Space

arXiv 2103.14756 ↗First posted 26 Mar 2021cs.CV eess.IV eess.SPcited by 83

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Abstract (arXiv)

In various imaging problems, we only have access to compressed measurements of the underlying signals, hindering most learning-based strategies which usually require pairs of signals and associated measurements for training. Learning only from compressed measurements is impossible in general, as the compressed observations do not contain information outside the range of the forward sensing operator. We propose a new end-to-end self-supervised framework that overcomes this limitation by exploiting the equivariances present in natural signals. Our proposed learning strategy performs as well as fully supervised methods. Experiments demonstrate the potential of this framework on inverse problems including sparse-view X-ray computed tomography on real clinical data and image inpainting on natural images. Code has been made available at: https://github.com/edongdongchen/EI.

Key facts. Cited by 83 papers in the map (data through 7 Oct 2026). Builds on 25 of its 40 references that are in the map. First posted on arXiv 26 Mar 2021.

Builds on

25 of 40 references.

References · 25

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  3. 2018ESRGAN: Enhanced Super-Resolution Generative Adversarial Networkscited by 1,250
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  6. 2016Least Squares Generative Adversarial Networkscited by 1,000
  7. 2018Free-Form Image Inpainting with Gated Convolutioncited by 594
  8. 2018Generative Image Inpainting with Contextual Attentioncited by 578
  9. 2018Noise2Noise: Learning Image Restoration without Clean Datacited by 526
  10. 2018Image Inpainting for Irregular Holes Using Partial Convolutionscited by 505
  11. 2016Deep Convolutional Neural Network for Inverse Problems in Imagingcited by 431
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13 more
  1. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 303
  2. 2019Noise2Self: Blind Denoising by Self-Supervisioncited by 274
  3. 2014Understanding image representations by measuring their equivariance and equivalencecited by 240
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  6. 2019Noisier2Noise: Learning to Denoise from Unpaired Noisy Datacited by 125
  7. 2019RARE: Image Reconstruction using Deep Priors Learned without Ground Truthcited by 64
  8. 2018Neural Proximal Gradient Descent for Compressive Imagingcited by 46
  9. 2016Generalization Error of Invariant Classifierscited by 42
  10. 2019Deep Decomposition Learning for Inverse Imaging Problemscited by 25
  11. 2020Improving Transformation Invariance in Contrastive Representation Learningcited by 16
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 12; 2023: 18; 2024: 16; 2025: 17; 2026: 18.

83 papers.

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  1. 2023Equivariant Multi-Modality Image Fusioncited by 98
  2. 2021Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurementscited by 56
  3. 2022Imaging with Equivariant Deep Learningcited by 35
  4. 2022Sensing Theorems for Unsupervised Learning in Linear Inverse Problemscited by 28
  5. 2023Equivariant plug-and-play image reconstructioncited by 26
  6. 2023What's in a Prior? Learned Proximal Networks for Inverse Problemscited by 24
  7. 2022Online Deep Equilibrium Learning for Regularization by Denoisingcited by 22
  8. 2022Transformer Meets Boundary Value Inverse Problemscited by 22
  9. 2022Unsupervised Learning From Incomplete Measurements for Inverse Problemscited by 20
  10. 2023Equivariant Bootstrapping for Uncertainty Quantification in Imaging Inverse Problemscited by 17
  11. 2023Scale-Equivariant Imaging: Self-Supervised Learning for Image Super-Resolution and Deblurringcited by 14
  12. 2024Diffusion Posterior Proximal Sampling for Image Restorationcited by 14
38 more
  1. 2024Generalized Recorrupted-to-Recorrupted: Self-Supervised Learning Beyond Gaussian Noisecited by 13
  2. 2023Self-Supervised Scalable Deep Compressed Sensingcited by 8
  3. 2023Deep Physics-Guided Unrolling Generalization for Compressed Sensingcited by 7
  4. 2025Measurement Score-Based Diffusion Modelcited by 7
  5. 2023Progressive Content-aware Coded Hyperspectral Compressive Imagingcited by 6
  6. 2023Auto-Linear Phenomenon in Subsurface Imagingcited by 6
  7. 2023MEPNet: A Model-Driven Equivariant Proximal Network for Joint Sparse-View Reconstruction and Metal Artifact Reduction in CT Imagescited by 6
  8. 2024Glimpse: Generalized Locality for Scalable and Robust CTcited by 6
  9. 2024QN-Mixer: A Quasi-Newton MLP-Mixer Model for Sparse-View CT Reconstructioncited by 6
  10. 2022Scale-Equivariant Unrolled Neural Networks for Data-Efficient Accelerated MRI Reconstructioncited by 5
  11. 2023Learning to Reconstruct Signals From Binary Measurementscited by 5
  12. 2023Unsupervised Spectral Demosaicing with Lightweight Spectral Attention Networkscited by 5
  13. 2024Perspective-Equivariance for Unsupervised Imaging with Camera Geometrycited by 5
  14. 2024Equivariant Imaging for Self-supervised Hyperspectral Image Inpaintingcited by 5
  15. 2025A Regularization-Guided Equivariant Approach for Image Restorationcited by 5
  16. 2026Self-Supervised Learning from Noisy and Incomplete Datacited by 5
  17. 2021Stochastic Primal-Dual Deep Unrollingcited by 4
  18. 2022D3C2-Net: Dual-Domain Deep Convolutional Coding Network for Compressive Sensingcited by 4
  19. 2023Unsupervised approaches based on optimal transport and convex analysis for inverse problems in imagingcited by 4
  20. 2025Benchmarking Self-Supervised Learning Methods for Accelerated MRI Reconstructioncited by 4
  21. 2025Sparsity-Driven Parallel Imaging Consistency for Improved Self-Supervised MRI Reconstructioncited by 4
  22. 2022Rotationally Equivariant Super-Resolution of Velocity Fields in Two-Dimensional Fluids Using Convolutional Neural Networkscited by 3
  23. 2022Improving Computed Tomography (CT) Reconstruction via 3D Shape Inductioncited by 3
  24. 2022Nonlinear Equivariant Imaging: Learning Multi-Parametric Tissue Mapping without Ground Truth for Compressive Quantitative MRIcited by 3
  25. 2024Unsupervised Training of Convex Regularizers using Maximum Likelihood Estimationcited by 3
  26. 2024Fully Unsupervised Dynamic MRI Reconstruction via Diffeo-Temporal Equivariancecited by 3
  27. 2025TomoSelfDEQ: Self-Supervised Deep Equilibrium Learning for Sparse-Angle CT Reconstructioncited by 3
  28. 2025NPN: Non-Linear Projections of the Null-Space for Imaging Inverse Problemscited by 3
  29. 2023Efficient Model-Based Deep Learning via Network Pruning and Fine-Tuningcited by 2
  30. 2024From Learning to Optimize to Learning Optimization Algorithmscited by 2
  31. 2024Segment as You Wish -- Free-Form Language-Based Segmentation for Medical Imagescited by 2
  32. 2024Fast MRI for All: Bridging Access Gaps by Training without Raw Datacited by 2
  33. 2025A Self-supervised Diffusion Bridge for MRI Reconstructioncited by 2
  34. 2026An analytic theory of convolutional neural network inverse problems solverscited by 2
  35. 2022Equivariance Regularization for Image Reconstructioncited by 1
  36. 2022Self-Supervised Deep Equilibrium Models for Inverse Problems with Theoretical Guaranteescited by 1
  37. 2023Single-photon Image Super-resolution via Self-supervised Learningcited by 1
  38. 2023SimPINNs: Simulation-Driven Physics-Informed Neural Networks for Enhanced Performance in Nonlinear Inverse Problemscited by 1

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