mlsanityData to 14 Oct 2026

A theoretical framework for self-supervised MR image reconstruction using sub-sampling via variable density Noisier2Noise

arXiv 2205.10278 ↗First posted 20 May 2022eess.IV cs.AIcited by 30

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Abstract (arXiv)

In recent years, there has been attention on leveraging the statistical modeling capabilities of neural networks for reconstructing sub-sampled Magnetic Resonance Imaging (MRI) data. Most proposed methods assume the existence of a representative fully-sampled dataset and use fully-supervised training. However, for many applications, fully sampled training data is not available, and may be highly impractical to acquire. The development and understanding of self-supervised methods, which use only sub-sampled data for training, are therefore highly desirable. This work extends the Noisier2Noise framework, which was originally constructed for self-supervised denoising tasks, to variable density sub-sampled MRI data. We use the Noisier2Noise framework to analytically explain the performance of Self-Supervised Learning via Data Undersampling (SSDU), a recently proposed method that performs well in practice but until now lacked theoretical justification. Further, we propose two modifications of SSDU that arise as a consequence of the theoretical developments. Firstly, we propose partitioning the sampling set so that the subsets have the same type of distribution as the original sampling mask. Secondly, we propose a loss weighting that compensates for the sampling and partitioning densities. On the fastMRI dataset we show that these changes significantly improve SSDU's image restoration quality and robustness to the partitioning parameters.

Key facts. Cited by 30 papers in the map (data through 14 Oct 2026). Builds on 32 of its 68 references that are in the map. First posted on arXiv 20 May 2022.

Builds on

32 of 68 references.

References · 32

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  3. 2017Deep Image Priorcited by 1,098
  4. 2018Noise2Noise: Learning Image Restoration without Clean Datacited by 533
  5. 2018fastMRI: An Open Dataset and Benchmarks for Accelerated MRIcited by 470
  6. 2017MoDL: Model Based Deep Learning Architecture for Inverse Problemscited by 387
  7. 2018Noise2Void - Learning Denoising from Single Noisy Imagescited by 364
  8. 2017Learning a Variational Network for Reconstruction of Accelerated MRI Datacited by 342
  9. 2019Noise2Self: Blind Denoising by Self-Supervisioncited by 276
  10. 2017Image reconstruction by domain transform manifold learningcited by 232
  11. 2020End-to-End Variational Networks for Accelerated MRI Reconstructioncited by 202
  12. 2019Noisier2Noise: Learning to Denoise from Unpaired Noisy Datacited by 126
20 more
  1. 2021Noise2Score: Tweedie's Approach to Self-Supervised Image Denoising without Clean Imagescited by 113
  2. 2016A deep convolutional neural network using directional wavelets for low-dose X-ray CT reconstructioncited by 87
  3. 2017Compressed Sensing MRI Reconstruction using a Generative Adversarial Network with a Cyclic Losscited by 82
  4. 2019Plug and play methods for magnetic resonance imaging (long version)cited by 75
  5. 2019Time-Dependent Deep Image Prior for Dynamic MRIcited by 70
  6. 2019RARE: Image Reconstruction using Deep Priors Learned without Ground Truthcited by 64
  7. 2020Noise2Same: Optimizing A Self-Supervised Bound for Image Denoisingcited by 56
  8. 2021Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurementscited by 56
  9. 2022Physics-Driven Deep Learning for Computational Magnetic Resonance Imagingcited by 50
  10. 2021AI-based Reconstruction for Fast MRI -- A Systematic Review and Meta-analysiscited by 38
  11. 2018DIMENSION: Dynamic MR Imaging with Both K-space and Spatial Prior Knowledge Obtained via Multi-Supervised Network Trainingcited by 26
  12. 2021Self-Supervised Learning for MRI Reconstruction with a Parallel Network Training Frameworkcited by 26
  13. 2020Unsupervised MRI Reconstruction with Generative Adversarial Networkscited by 24
  14. 2020Multi-Mask Self-Supervised Learning for Physics-Guided Neural Networks in Highly Accelerated MRIcited by 14
  15. 2021Deformation-Compensated Learning for Image Reconstruction without Ground Truthcited by 9
  16. 2022PARCEL: Physics-based Unsupervised Contrastive Representation Learning for Multi-coil MR Imagingcited by 8
  17. 2019Deep Plug-and-Play Prior for Parallel MRI Reconstructioncited by 3
  18. 2020Improved Supervised Training of Physics-Guided Deep Learning Image Reconstruction with Multi-Maskingcited by 3
  19. 2016Astronomical image reconstruction with convolutional neural networkscited by 1
  20. 2021MRI Recovery with A Self-calibrated Denoisercited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 6; 2024: 5; 2025: 11; 2026: 8.

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  1. 2023Ambient Diffusion: Learning Clean Distributions from Corrupted Datacited by 111
  2. 2024Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Datacited by 32
  3. 2023Analyzing the Sample Complexity of Self-Supervised Image Reconstruction Methodscited by 8
  4. 2023Self-Supervised Scalable Deep Compressed Sensingcited by 8
  5. 2025Measurement Score-Based Diffusion Modelcited by 8
  6. 2023A Deep Learning Method for Simultaneous Denoising and Missing Wedge Reconstruction in Cryogenic Electron Tomographycited by 7
  7. 2023K-band: Self-supervised MRI Reconstruction via Stochastic Gradient Descent over K-space Subsetscited by 6
  8. 2025Noisier2Inverse: Self-Supervised Learning for Image Reconstruction with Correlated Noisecited by 5
  9. 2026Self-Supervised Learning from Noisy and Incomplete Datacited by 5
  10. 2023Joint Supervised and Self-supervised Learning for MRI Reconstructioncited by 4
  11. 2024Robust multi-coil MRI reconstruction via self-supervised denoisingcited by 4
  12. 2025Benchmarking Self-Supervised Learning Methods for Accelerated MRI Reconstructioncited by 4
18 more
  1. 2025Sparsity-Driven Parallel Imaging Consistency for Improved Self-Supervised MRI Reconstructioncited by 4
  2. 2024Deep Learning-based Accelerated MR Cholangiopancreatography without Fully-sampled Datacited by 2
  3. 2024MotionTTT: 2D Test-Time-Training Motion Estimation for 3D Motion Corrected MRIcited by 2
  4. 2024Fast MRI for All: Bridging Access Gaps by Training without Raw Datacited by 2
  5. 2025Re-Visible Dual-Domain Self-Supervised Deep Unfolding Network for MRI Reconstructioncited by 1
  6. 2025Equivariant Splitting: Self-supervised learning from incomplete datacited by 1
  7. 2025UPMRI: Unsupervised Parallel MRI Reconstruction via Projected Conditional Flow Matchingcited by 1
  8. 2025An Adaptive, Disentangled Representation for Multidimensional MRI Reconstructioncited by 1
  9. 2025Extendable Generalization Self-Supervised Diffusion for Low-Dose CT Reconstructioncited by 0
  10. 2025MID: A Self-supervised Multimodal Iterative Denoising Frameworkcited by 0
  11. 2025Locally-Supervised Global Image Restorationcited by 0
  12. 2026HyDRA: Hybrid Denoising Regularization for Measurement-Only DEQ Trainingcited by 0
  13. 2026Accelerating Stroke MRI with Diffusion Probabilistic Models through Large-Scale Pre-training and Target-Specific Fine-Tuningcited by 0
  14. 2026Self-Supervised Uncertainty Estimation For Super-Resolution of Satellite Imagescited by 0
  15. 2026Self-Supervised Angular Deblurring in Photoacoustic Reconstruction via Noisier2Inversecited by 0
  16. 2026CoilDrop-MRI: Self-supervised physics-guided MRI reconstruction with coil dropoutcited by 0
  17. 2026Enhancing Implicit Neural Representations with Image Feature Embedding for Unsupervised Cardiac Cine MRI Reconstructioncited by 0
  18. 2026Hankel Subspace Self-Supervised Learning for Parallel MRI Reconstructioncited by 0