mlsanityData to 7 Oct 2026

A Conditional Normalizing Flow for Accelerated Multi-Coil MR Imaging

arXiv 2306.01630 ↗First posted 2 Jun 2023eess.IV cs.CVcited by 10

Not on the map. Why?

Abstract (arXiv)

Accelerated magnetic resonance (MR) imaging attempts to reduce acquisition time by collecting data below the Nyquist rate. As an ill-posed inverse problem, many plausible solutions exist, yet the majority of deep learning approaches generate only a single solution. We instead focus on sampling from the posterior distribution, which provides more comprehensive information for downstream inference tasks. To do this, we design a novel conditional normalizing flow (CNF) that infers the signal component in the measurement operator's nullspace, which is later combined with measured data to form complete images. Using fastMRI brain and knee data, we demonstrate fast inference and accuracy that surpasses recent posterior sampling techniques for MRI. Code is available at https://github.com/jwen307/mri_cnf/

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 35 of its 54 references that are in the map. First posted on arXiv 2 Jun 2023.

Builds on

35 of 54 references.

References · 35

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  4. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  5. 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,267
  6. 2016Image-to-Image Translation with Conditional Adversarial Networkscited by 4,510
  7. 2016Density estimation using Real NVPcited by 2,029
  8. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
  9. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  10. 2014NICE: Non-linear Independent Components Estimationcited by 1,052
  11. 2020A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challengescited by 813
  12. 2018fastMRI: An Open Dataset and Benchmarks for Accelerated MRIcited by 464
23 more
  1. 2017Learning a Variational Network for Reconstruction of Accelerated MRI Datacited by 340
  2. 2017Compressed Sensing using Generative Modelscited by 337
  3. 2021Score-based diffusion models for accelerated MRIcited by 308
  4. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  5. 2020SRFlow: Learning the Super-Resolution Space with Normalizing Flowcited by 209
  6. 2020End-to-End Variational Networks for Accelerated MRI Reconstructioncited by 201
  7. 2019Learning Likelihoods with Conditional Normalizing Flowscited by 170
  8. 2019Guided Image Generation with Conditional Invertible Neural Networkscited by 147
  9. 2018Explaining Image Classifiers by Counterfactual Generationcited by 144
  10. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 96
  11. 2019Deep Learning Methods for Parallel Magnetic Resonance Image Reconstructioncited by 81
  12. 2020Solving Linear Inverse Problems Using the Prior Implicit in a Denoisercited by 78
  13. 2016Amortised MAP Inference for Image Super-resolutioncited by 68
  14. 2018Deep Bayesian Inversioncited by 60
  15. 2019Uncertainty Quantification in Deep MRI Reconstructioncited by 49
  16. 2019Deep Decomposition Learning for Inverse Imaging Problemscited by 25
  17. 2021Conditional Invertible Neural Networks for Diverse Image-to-Image Translationcited by 24
  18. 2018Scalable Bayesian uncertainty quantification in imaging inverse problems via convex optimizationcited by 22
  19. 2021Noise Conditional Flow Model for Learning the Super-Resolution Spacecited by 19
  20. 2021Conditional Invertible Neural Networks for Medical Imagingcited by 19
  21. 2021Conditional Frechet Inception Distancecited by 16
  22. 2022FS-NCSR: Increasing Diversity of the Super-Resolution Space via Frequency Separation and Noise-Conditioned Normalizing Flowcited by 8
  23. 2022Technical Report (v1.0)--Pseudo-random Cartesian Sampling for Dynamic MRIcited by 8

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 3; 2025: 4; 2026: 1.

10 papers.

  1. 2023WISE: full-Waveform variational Inference via Subsurface Extensionscited by 10
  2. 2023Solving multiphysics-based inverse problems with learned surrogates and constraintscited by 9
  3. 2024Task-Driven Uncertainty Quantification in Inverse Problems via Conformal Predictioncited by 8
  4. 2024MRI Reconstruction with Regularized 3D Diffusion Model (R3DM)cited by 4
  5. 2024pcaGAN: Improving Posterior-Sampling cGANs via Principal Component Regularizationcited by 2
  6. 2025Conformal Bounds on Full-Reference Image Quality for Imaging Inverse Problemscited by 2
  7. 2025Advancing MRI Reconstruction: A Systematic Review of Deep Learning and Compressed Sensing Integrationcited by 0
  8. 2025Active MRI Acquisition with Diffusion Guided Bayesian Experimental Designcited by 0
  9. 2025Minimax Multi-Target Conformal Prediction with Applications to Imaging Inverse Problemscited by 0
  10. 2026Separating Intrinsic Ambiguity from Estimation Uncertainty in Deep Generative Models for Linear Inverse Problemscited by 0