mlsanityData to 7 Oct 2026

Learning a Variational Network for Reconstruction of Accelerated MRI Data

arXiv 1704.00447 ↗First posted 3 Apr 2017cs.CVcited by 340

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Cited by 40 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Purpose: To allow fast and high-quality reconstruction of clinical accelerated multi-coil MR data by learning a variational network that combines the mathematical structure of variational models with deep learning. Theory and Methods: Generalized compressed sensing reconstruction formulated as a variational model is embedded in an unrolled gradient descent scheme. All parameters of this formulation, including the prior model defined by filter kernels and activation functions as well as the data term weights, are learned during an offline training procedure. The learned model can then be applied online to previously unseen data. Results: The variational network approach is evaluated on a clinical knee imaging protocol. The variational network reconstructions outperform standard reconstruction algorithms in terms of image quality and residual artifacts for all tested acceleration factors and sampling patterns. Conclusion: Variational network reconstructions preserve the natural appearance of MR images as well as pathologies that were not included in the training data set. Due to its high computational performance, i.e., reconstruction time of 193 ms on a single graphics card, and the omission of parameter tuning once the network is trained, this new approach to image reconstruction can easily be integrated into clinical workflow.

Key facts. Cited by 340 papers in the map (data through 7 Oct 2026). First posted on arXiv 3 Apr 2017.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 63; 2022: 74; 2023: 69; 2024: 44; 2025: 48; 2026: 42.

340 papers.

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  1. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  2. 2022Adaptive Diffusion Priors for Accelerated MRI Reconstructioncited by 117
  3. 2022Monarch: Expressive Structured Matrices for Efficient and Accurate Trainingcited by 100
  4. 2021Unsupervised MRI Reconstruction via Zero-Shot Learned Adversarial Transformerscited by 76
  5. 2022Conversion Between CT and MRI Images Using Diffusion and Score-Matching Modelscited by 69
  6. 2025InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciencescited by 67
  7. 2022Measurement-conditioned Denoising Diffusion Probabilistic Model for Under-sampled Medical Image Reconstructioncited by 64
  8. 2024Learning Diffusion Priors from Observations by Expectation Maximizationcited by 60
  9. 2022Towards performant and reliable undersampled MR reconstruction via diffusion model samplingcited by 59
  10. 2021Task Transformer Network for Joint MRI Reconstruction and Super-Resolutioncited by 58
  11. 2021Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurementscited by 56
  12. 2021Can stable and accurate neural networks be computed? -- On the barriers of deep learning and Smale's 18th problemcited by 53
38 more
  1. 2021Zero-Shot Self-Supervised Learning for MRI Reconstructioncited by 53
  2. 2022Physics-Driven Deep Learning for Computational Magnetic Resonance Imagingcited by 49
  3. 2022Bayesian MRI Reconstruction with Joint Uncertainty Estimation using Diffusion Modelscited by 46
  4. 2022Learned reconstruction methods with convergence guaranteescited by 46
  5. 2021Multi-Modal Transformer for Accelerated MR Imagingcited by 42
  6. 2022SKM-TEA: A Dataset for Accelerated MRI Reconstruction with Dense Image Labels for Quantitative Clinical Evaluationcited by 42
  7. 2023GSURE-Based Diffusion Model Training with Corrupted Datacited by 40
  8. 2021AI-based Reconstruction for Fast MRI -- A Systematic Review and Meta-analysiscited by 38
  9. 2021Specificity-Preserving Federated Learning for MR Image Reconstructioncited by 35
  10. 2022Neural Implicit k-Space for Binning-free Non-Cartesian Cardiac MR Imagingcited by 35
  11. 2021Recurrent Variational Network: A Deep Learning Inverse Problem Solver applied to the task of Accelerated MRI Reconstructioncited by 34
  12. 2022Federated Learning of Generative Image Priors for MRI Reconstructioncited by 33
  13. 2024Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Datacited by 32
  14. 2021Bayesian Uncertainty Estimation of Learned Variational MRI Reconstructioncited by 30
  15. 2022DSFormer: A Dual-domain Self-supervised Transformer for Accelerated Multi-contrast MRI Reconstructioncited by 30
  16. 2022HUMUS-Net: Hybrid unrolled multi-scale network architecture for accelerated MRI reconstructioncited by 30
  17. 2021fastMRI+: Clinical Pathology Annotations for Knee and Brain Fully Sampled Multi-Coil MRI Datacited by 29
  18. 2022A theoretical framework for self-supervised MR image reconstruction using sub-sampling via variable density Noisier2Noisecited by 29
  19. 2021One-dimensional Deep Low-rank and Sparse Network for Accelerated MRIcited by 27
  20. 2021Learning the optimal Tikhonov regularizer for inverse problemscited by 26
  21. 2021Self-Supervised Learning for MRI Reconstruction with a Parallel Network Training Frameworkcited by 26
  22. 2021Learning a Model-Driven Variational Network for Deformable Image Registrationcited by 25
  23. 2023IMJENSE: Scan-specific Implicit Representation for Joint Coil Sensitivity and Image Estimation in Parallel MRIcited by 22
  24. 2022Stable Deep MRI Reconstruction using Generative Priorscited by 21
  25. 2023Diffusion Modeling with Domain-conditioned Prior Guidance for Accelerated MRI and qMRI Reconstructioncited by 20
  26. 2023CMRxRecon: An open cardiac MRI dataset for the competition of accelerated image reconstructioncited by 20
  27. 2021Deep J-Sense: Accelerated MRI Reconstruction via Unrolled Alternating Optimizationcited by 19
  28. 2021Learning Regularization Parameters of Inverse Problems via Deep Neural Networkscited by 19
  29. 2021SOUP-GAN: Super-Resolution MRI Using Generative Adversarial Networkscited by 18
  30. 2021Known Operator Learning and Hybrid Machine Learning in Medical Imaging -- A Review of the Past, the Present, and the Futurecited by 18
  31. 2021An Optimization-Based Meta-Learning Model for MRI Reconstruction with Diverse Datasetcited by 18
  32. 2025Solving Inverse Problems with FLAIRcited by 16
  33. 2021Universal Undersampled MRI Reconstructioncited by 15
  34. 2023MRI Reconstruction with Side Information using Diffusion Modelscited by 15
  35. 2023SMRD: SURE-based Robust MRI Reconstruction with Diffusion Modelscited by 15
  36. 2022On learning adaptive acquisition policies for undersampled multi-coil MRI reconstructioncited by 14
  37. 2022Scaling Laws For Deep Learning Based Image Reconstructioncited by 14
  38. 2021End-to-End Sequential Sampling and Reconstruction for MRIcited by 13

50 most cited of 340 All 340 (JSON)