pith. sign in

arxiv: 2508.14950 · v2 · pith:ZC3MPSAOnew · submitted 2025-08-20 · 📡 eess.IV · cs.LG

Potential and challenges of generative adversarial networks for super-resolution in 4D Flow MRI

Oliver Welin Odeback , Arivazhagan Geetha Balasubramanian , Jonas Schollenberger , Edward Ferdiand , Alistair A. Young , C. Alberto Figueroa , Susanne Schnell , Outi Tammisola
show 4 more authors
Ricardo Vinuesa Tobias Granberg Alexander Fyrdahl David Marlevi
This is my paper

Pith reviewed 2026-05-18 22:17 UTC · model grok-4.3

classification 📡 eess.IV cs.LG
keywords 4D Flow MRIsuper-resolutiongenerative adversarial networksWasserstein GANnear-wall velocitycerebrovascular flowhemodynamic imaging
0
0 comments X

The pith

A Wasserstein GAN improves near-wall velocity recovery in 4D Flow MRI super-resolution while maintaining stable training.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper tests whether generative adversarial networks can sharpen low-resolution 4D Flow MRI data to recover accurate blood velocities close to vessel walls. Training and testing rely on synthetic images created from patient-specific computer models of brain blood flow passed through a realistic MRI simulation pipeline. Across different adversarial loss functions, the Wasserstein variant yields lower velocity errors than a plain generator network and stays stable where other GANs do not. A sympathetic reader would care because better near-wall measurements could make 4D Flow MRI more reliable for estimating forces on vessel walls in conditions such as aneurysms or stroke.

Core claim

The proposed GAN architecture with Wasserstein adversarial loss improves near-wall velocity accuracy in super-resolved 4D Flow MRI, achieving a velocity normalized root mean square error of 6.9 percent compared to 9.6 percent for a non-adversarial reference and 7.2 percent for generator-only training, while also outperforming the baseline at low signal-to-noise ratios.

What carries the argument

A dedicated GAN trained on synthetic 4D Flow MRI images generated from in-silico cerebrovascular models via an MR-true reconstruction pipeline, evaluated with Vanilla, Relativistic, and Wasserstein adversarial losses.

Load-bearing premise

Synthetic images generated from patient-specific in-silico cerebrovascular models are sufficiently representative of real clinical 4D Flow MRI acquisitions for both training and quantitative evaluation of velocity accuracy.

What would settle it

Apply the trained models to real patient 4D Flow MRI scans and compare the recovered near-wall velocities against independent high-resolution reference measurements such as computational fluid dynamics simulations matched to the same anatomy.

Figures

Figures reproduced from arXiv: 2508.14950 by Alexander Fyrdahl, Alistair A. Young, Arivazhagan Geetha Balasubramanian, C. Alberto Figueroa, David Marlevi, Edward Ferdiand, Jonas Schollenberger, Oliver Welin Odeback, Outi Tammisola, Ricardo Vinuesa, Susanne Schnell, Tobias Granberg.

Figure 1
Figure 1. Figure 1: Overview of the dual-venc reconstruction and synthetic 4D Flow MRI generation process. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overview of the proposed GAN architecture. The generator accepts cubic patches as input and incorporates [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (A) Training and validation mean relative error (MRE) over 200 epochs. The first 100 epochs correspond to generator-only training (GAN-Gen). For subsequent epochs, adversarial losses are introduced. (B) Effect of varying adversarial loss weight (λG) of WGAN loss curves. the same MRE training curves, however when varying the generator adversarial loss of the WGAN setup for weight λG ∈ {10−4 , 10−3 , 10−2 }.… view at source ↗
Figure 4
Figure 4. Figure 4: Discriminator (LD) and generator loss (LG and LGen) trajectories for Vanilla, Relativistic, and WGANs under two regimes: without adversarial feedback (λG = 0, first column), and with adversarial feedback (λG = 10−3 , remaining columns) [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Qualitative comparison between low resolution (LR), high resolution (HR) and super-resolution (SR) at [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Qualitative comparison between low resolution (LR), high resolution (HR) and super-resolution (SR) with [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Boundary error visualization for 4DFlowNet, GAN-Gen, and WGAN under high and low SNR. Error maps [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Representative cross-sectional velocity fields and corresponding error maps illustrating weight interpolation [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: PCA projections of internal features for GAN-Gen, Vanilla, Relativistic, and WGAN networks, using 10,000 [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
read the original abstract

4D Flow Magnetic Resonance Imaging (4D Flow MRI) enables non-invasive quantification of blood flow and hemodynamic parameters. However, its clinical application is limited by low spatial resolution and noise, particularly affecting near-wall velocity measurements. Machine learning-based super-resolution has shown promise in addressing these limitations, but challenges remain, not least in recovering near-wall velocities. Generative adversarial networks (GANs) offer a compelling solution, having demonstrated strong capabilities in restoring sharp boundaries in non-medical super-resolution tasks. Yet, their application in 4D Flow MRI remains unexplored, with implementation challenged by known issues such as training instability and non-convergence. In this study, we investigate GAN-based super-resolution in 4D Flow MRI. Training and validation were conducted using patient-specific cerebrovascular in-silico models, converted into synthetic images via an MR-true reconstruction pipeline. A dedicated GAN architecture was implemented and evaluated across three adversarial loss functions: Vanilla, Relativistic, and Wasserstein. Our results demonstrate that the proposed GAN improved near-wall velocity recovery compared to a non-adversarial reference (vNRMSE: 6.9% vs. 9.6%); however, that implementation specifics are critical for stable network training. While Vanilla and Relativistic GANs proved unstable compared to generator-only training (vNRMSE: 8.1% and 7.8% vs. 7.2%), a Wasserstein GAN demonstrated optimal stability and incremental improvement (vNRMSE: 6.9% vs. 7.2%). The Wasserstein GAN further outperformed the generator-only baseline at low SNR (vNRMSE: 8.7% vs. 10.7%). These findings highlight the potential of GAN-based super-resolution in enhancing 4D Flow MRI, particularly in challenging cerebrovascular regions, while emphasizing the need for careful selection of adversarial strategies.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript investigates GAN-based super-resolution for 4D Flow MRI to improve near-wall velocity recovery, using synthetic images generated from patient-specific in-silico cerebrovascular models via an MR-true reconstruction pipeline. It implements a dedicated GAN and compares Vanilla, Relativistic, and Wasserstein adversarial losses against a generator-only baseline, reporting vNRMSE improvements (6.9% vs. 9.6% for non-adversarial reference) and noting that Wasserstein GAN offers better stability and performance at low SNR (8.7% vs. 10.7%).

Significance. If the synthetic-data gains translate, the work provides concrete evidence that adversarial training can enhance velocity accuracy in low-resolution 4D Flow MRI, with practical guidance on loss-function choice to avoid instability. The controlled in-silico setup enables precise quantitative evaluation that is difficult to obtain in vivo.

major comments (2)
  1. [Abstract] Abstract: the central claim that GAN super-resolution addresses clinical limitations in near-wall velocity measurement rests entirely on metrics computed inside a closed synthetic loop (in-silico models passed through the same MR-true pipeline used for training). This does not establish robustness to the distinct noise spectra, partial-volume effects, and flow-boundary conditions of real patient 4D Flow MRI acquisitions.
  2. [Results] Results (vNRMSE comparisons): the reported differences (e.g., 6.9% vs. 7.2% for Wasserstein vs. generator-only) are given without error bars, confidence intervals, or the number of independent test volumes, making it impossible to judge whether the incremental improvement is statistically reliable or reproducible across different cerebrovascular geometries.
minor comments (1)
  1. [Abstract] Abstract: the phrase 'implementation specifics are critical for stable network training' is stated but not supported by any hyperparameter table or training-curve description in the provided text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review of our manuscript on GAN-based super-resolution for 4D Flow MRI. We have addressed each major comment point by point below. Revisions have been made to clarify the scope of the synthetic evaluation and to improve the statistical reporting of results.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that GAN super-resolution addresses clinical limitations in near-wall velocity measurement rests entirely on metrics computed inside a closed synthetic loop (in-silico models passed through the same MR-true pipeline used for training). This does not establish robustness to the distinct noise spectra, partial-volume effects, and flow-boundary conditions of real patient 4D Flow MRI acquisitions.

    Authors: We agree that the evaluation is conducted entirely within a synthetic data framework using patient-specific in-silico cerebrovascular models and an MR-true reconstruction pipeline. This controlled setup was deliberately chosen to provide exact ground-truth velocities for quantitative assessment, which is not feasible in real acquisitions. The referee is correct that this does not directly prove robustness to the noise spectra, partial-volume effects, or boundary conditions encountered in actual patient 4D Flow MRI. In the revised manuscript we have updated the abstract to explicitly note the synthetic nature of the data and added a new paragraph in the Discussion section that acknowledges these limitations and outlines planned future work on real patient datasets. revision: yes

  2. Referee: [Results] Results (vNRMSE comparisons): the reported differences (e.g., 6.9% vs. 7.2% for Wasserstein vs. generator-only) are given without error bars, confidence intervals, or the number of independent test volumes, making it impossible to judge whether the incremental improvement is statistically reliable or reproducible across different cerebrovascular geometries.

    Authors: We thank the referee for highlighting this omission. The original submission presented only mean vNRMSE values. We have revised the Results section to report standard deviations as error bars for all vNRMSE comparisons, to state that the test set comprises 12 independent volumes derived from distinct patient-specific cerebrovascular geometries, and to include a brief statement on cross-geometry consistency. These additions allow readers to evaluate the reliability and reproducibility of the reported improvements. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical evaluation on independently generated synthetic data

full rationale

The paper reports experimental results from training and testing GAN variants on synthetic 4D Flow MRI images derived from patient-specific in-silico cerebrovascular models via an MR-true reconstruction pipeline. Performance metrics such as vNRMSE are computed by direct comparison of network outputs against the known high-resolution ground-truth velocities in held-out synthetic cases. No equations, derivations, or self-citations are invoked that would reduce these metrics to fitted parameters defined by the same experiment or to any self-referential construction. The evaluation follows standard supervised learning practice with an external synthetic benchmark, rendering the reported improvements (e.g., 6.9% vs. 9.6%) independent of any load-bearing circular step.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central performance claims rest on the fidelity of the synthetic data generation process and the assumption that velocity error metrics on synthetic test cases translate to clinical utility.

free parameters (1)
  • Choice of adversarial loss function
    Vanilla, Relativistic, and Wasserstein variants were selected and compared; the Wasserstein variant was retained after observing superior stability.
axioms (1)
  • domain assumption Synthetic MR-true images from in-silico cerebrovascular models accurately capture the noise and resolution characteristics of real 4D Flow MRI acquisitions
    All training and validation rely on this equivalence for quantitative vNRMSE evaluation.

pith-pipeline@v0.9.0 · 5931 in / 1399 out tokens · 45489 ms · 2026-05-18T22:17:46.330190+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

76 extracted references · 76 canonical work pages · 2 internal anchors

  1. [1]

    Kappeler, S

    A. Kappeler, S. Yoo, Q. Dai, A. K. Katsaggelos, Video super-resolution with convolutional neural networks, IEEE transactions on computa- tional imaging 2 (2) (2016) 109–122

    work page 2016

  2. [2]

    Z. Wang, J. Chen, S. C. Hoi, Deep learning for image super-resolution: A survey, IEEE transactions on pattern analysis and machine intelligence 43 (10) (2020) 3365–3387

    work page 2020

  3. [3]

    Y . Li, B. Sixou, F. Peyrin, A review of the deep learning methods for medical images super resolution problems, Irbm 42 (2) (2021) 120–133

    work page 2021

  4. [4]

    H. Hou, H. Andrews, Cubic splines for image interpolation and digital filtering, IEEE Transactions on acoustics, speech, and signal processing 26 (6) (1978) 508–517

    work page 1978

  5. [5]

    Keys, Cubic convolution interpolation for digital image processing, IEEE transactions on acoustics, speech, and signal processing 29 (6) (2003) 1153–1160

    R. Keys, Cubic convolution interpolation for digital image processing, IEEE transactions on acoustics, speech, and signal processing 29 (6) (2003) 1153–1160

    work page 2003

  6. [6]

    S. C. Park, M. K. Park, M. G. Kang, Super-resolution image reconstruction: a technical overview, IEEE signal processing magazine 20 (3) (2003) 21–36

    work page 2003

  7. [7]

    C. Dong, C. C. Loy, K. He, X. Tang, Image super-resolution using deep convolutional networks, IEEE transactions on pattern analysis and machine intelligence 38 (2) (2015) 295–307

    work page 2015

  8. [8]

    J. Kim, J. K. Lee, K. M. Lee, Accurate image super-resolution using very deep convolutional networks, in: Proceedings of the IEEE confer- ence on computer vision and pattern recognition, 2016, pp. 1646–1654

    work page 2016

  9. [9]

    T. Tong, G. Li, X. Liu, Q. Gao, Image super-resolution using dense skip connections, in: Proceedings of the IEEE international conference on computer vision, 2017, pp. 4799–4807. 20

    work page 2017

  10. [10]

    Ledig, L

    C. Ledig, L. Theis, F. Huszar, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. Tejani, J. Totz, Z. Wang, et al., Photo-realistic single image super-resolution using a generative adversarial network, in: Proceedings of the IEEE conference on computer vision and pattern recognition, 2017, pp. 4681–4690

    work page 2017

  11. [11]

    M. S. Sajjadi, B. Scholkopf, M. Hirsch, Enhancenet: Single image super-resolution through automated texture synthesis, in: Proceedings of the IEEE international conference on computer vision, 2017, pp. 4491–4500

    work page 2017

  12. [12]

    X. Wang, K. Yu, S. Wu, J. Gu, Y . Liu, C. Dong, Y . Qiao, C. Change Loy, Esrgan: Enhanced super-resolution generative adversarial networks, in: Proceedings of the European conference on computer vision (ECCV) workshops, 2018, pp. 0–0

    work page 2018

  13. [13]

    Karnewar, O

    A. Karnewar, O. Wang, Msg-gan: Multi-scale gradients for generative adversarial networks, in: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2020, pp. 7799–7808

    work page 2020

  14. [14]

    Liang, H

    J. Liang, H. Zeng, L. Zhang, Details or artifacts: A locally discriminative learning approach to realistic image super-resolution, in: Proceed- ings of the IEEE/CVF conference on computer vision and pattern recognition, 2022, pp. 5657–5666

    work page 2022

  15. [15]

    Z. Lu, J. Li, H. Liu, C. Huang, L. Zhang, T. Zeng, Transformer for single image super-resolution, in: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2022, pp. 457–466

    work page 2022

  16. [16]

    Goodfellow, J

    I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, Y . Bengio, Generative adversarial networks, in: Advances in Neural Information Processing Systems (NeurIPS), V ol. 27, 2014, pp. 2672–2680

    work page 2014

  17. [17]

    The relativistic discriminator: a key element missing from standard GAN

    A. Jolicoeur-Martineau, The relativistic discriminator: a key element missing from standard gan, arXiv preprint arXiv:1807.00734 (2018)

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  18. [18]

    Vinuesa, S

    R. Vinuesa, S. L. Brunton, B. J. McKeon, The transformative potential of machine learning for experiments in fluid mechanics, Nature Reviews Physics 5 (9) (2023) 536–545

    work page 2023

  19. [19]

    C.-H. Pham, C. Tor-D ´ıez, H. Meunier, N. Bednarek, R. Fablet, N. Passat, F. Rousseau, Multiscale brain mri super-resolution using deep 3d convolutional networks, Computerized Medical Imaging and Graphics 77 (2019) 101647

    work page 2019

  20. [20]

    J. Park, D. Hwang, K. Y . Kim, S. K. Kang, Y . K. Kim, J. S. Lee, Computed tomography super-resolution using deep convolutional neural network, Physics in Medicine & Biology 63 (14) (2018) 145011

    work page 2018

  21. [21]

    Christensen-Jeffries, O

    K. Christensen-Jeffries, O. Couture, P. A. Dayton, Y . C. Eldar, K. Hynynen, F. Kiessling, M. O’Reilly, G. F. Pinton, G. Schmitz, M.-X. Tang, et al., Super-resolution ultrasound imaging, Ultrasound in medicine & biology 46 (4) (2020) 865–891

    work page 2020

  22. [22]

    Markl, A

    M. Markl, A. Frydrychowicz, S. Kozerke, M. Hope, O. Wieben, 4d flow mri, Journal of Magnetic Resonance Imaging 36 (5) (2012) 1015– 1036

    work page 2012

  23. [23]

    Stankovic, B

    Z. Stankovic, B. Jung, J. Collins, M. F. Russe, J. Carr, W. Euringer, L. Stehlin, Z. Csatari, P. C. Strohm, M. Langer, et al., Reproducibility study of four-dimensional flow mri of arterial and portal venous liver hemodynamics: Influence of spatio-temporal resolution, Magnetic resonance in medicine 72 (2) (2014) 477–484

    work page 2014

  24. [24]

    Aristova, A

    M. Aristova, A. Vali, S. A. Ansari, A. Shaibani, T. D. Alden, M. C. Hurley, B. S. Jahromi, M. B. Potts, M. Markl, S. Schnell, Standardized evaluation of cerebral arteriovenous malformations using flow distribution network graphs and dual-venc 4d flow mri, Journal of Magnetic Resonance Imaging 50 (6) (2019) 1718–1730

    work page 2019

  25. [25]

    Marlevi, J

    D. Marlevi, J. Schollenberger, M. Aristova, E. Ferdian, Y . Ma, A. A. Young, E. R. Edelman, S. Schnell, C. A. Figueroa, D. A. Nordsletten, Noninvasive quantification of cerebrovascular pressure changes using 4d flow mri, Magnetic resonance in medicine 86 (6) (2021) 3096–3110

    work page 2021

  26. [26]

    Hyodo, Y

    R. Hyodo, Y . Takehara, S. Naganawa, 4d flow mri in the portal venous system: imaging and analysis methods, and clinical applications, La radiologia medica 127 (11) (2022) 1181–1198

    work page 2022

  27. [27]

    Schnell, C

    S. Schnell, C. Wu, S. A. Ansari, Four-dimensional mri flow examinations in cerebral and extracerebral vessels–ready for clinical routine?, Current opinion in neurology 29 (4) (2016) 419–428

    work page 2016

  28. [28]

    Aristova, J

    M. Aristova, J. Pang, Y . Ma, L. Ma, H. Berhane, V . Rayz, M. Markl, S. Schnell, Accelerated dual-venc 4d flow mri with variable high-venc spatial resolution for neurovascular applications, Magnetic resonance in medicine 88 (4) (2022) 1643–1658

    work page 2022

  29. [29]

    Gottwald, J

    L. Gottwald, J. T ¨oger, K. M. Bloch, E. Peper, B. Coolen, G. Strijkers, P. Van Ooij, A. Nederveen, High spatiotemporal resolution 4d flow mri of intracranial aneurysms at 7t in 10 minutes, American Journal of Neuroradiology 41 (7) (2020) 1201–1208

    work page 2020

  30. [30]

    M. F. Fathi, I. Perez-Raya, A. Baghaie, P. Berg, G. Janiga, A. Arzani, R. M. D’Souza, Super-resolution and denoising of 4d-flow mri using physics-informed deep neural nets, Computer Methods and Programs in Biomedicine 197 (2020) 105729

    work page 2020

  31. [31]

    Ferdian, A

    E. Ferdian, A. Suinesiaputra, D. J. Dubowitz, D. Zhao, A. Wang, B. Cowan, A. A. Young, 4dflownet: Super-resolution 4d flow mri using deep learning and computational fluid dynamics, Frontiers in Physics 8 (2020)

    work page 2020

  32. [32]

    Ferdian, D

    E. Ferdian, D. Marlevi, J. Schollenberger, M. Aristova, E. Edelman, S. Schnell, C. Figueroa, D. Nordsletten, A. Young, Cerebrovascular super-resolution 4d flow mri – sequential combination of resolution enhancement by deep learning and physics-informed image processing to non-invasively quantify intracranial velocity, flow, and relative pressure, Medical ...

    work page 2023

  33. [33]

    S. Shit, J. Zimmermann, I. Ezhov, J. C. Paetzold, A. F. Sanches, C. Pirkl, B. H. Menze, Srflow: Deep learning based super-resolution of 4d-flow mri data, Frontiers in Artificial Intelligence 5 (2022) 928181

    work page 2022

  34. [34]

    Saitta, M

    S. Saitta, M. Carioni, S. Mukherjee, C.-B. Sch ¨onlieb, A. Redaelli, Implicit neural representations for unsupervised super-resolution and denoising of 4d flow mri, Computer methods and programs in biomedicine 246 (2024) 108057

    work page 2024

  35. [35]

    Rutkowski, A

    D. Rutkowski, A. Rold ´an-Alzate, K. Johnson, Enhancement of cerebrovascular 4d flow mri velocity fields using machine learning and computational fluid dynamics simulation data, Nature Scientific Reports 11 (2021) 10240

    work page 2021

  36. [36]

    Szajer, K

    J. Szajer, K. Ho-Shon, A comparison of 4d flow mri-derived wall shear stress with computational fluid dynamics methods for intracranial aneurysms and carotid bifurcations—a review, Magnetic resonance imaging 48 (2018) 62–69

    work page 2018

  37. [37]

    G ¨uemes, S

    A. G ¨uemes, S. Discetti, A. Ianiro, B. Sirmacek, H. Azizpour, R. Vinuesa, From coarse wall measurements to turbulent velocity fields through deep learning, Physics of fluids 33 (7) (2021)

    work page 2021

  38. [38]

    M. Z. Yousif, L. Yu, S. Hoyas, R. Vinuesa, H. Lim, A deep-learning approach for reconstructing 3d turbulent flows from 2d observation data, Scientific Reports 13 (1) (2023) 2529

    work page 2023

  39. [39]

    C. You, G. Li, Y . Zhang, X. Zhang, H. Shan, M. Li, S. Ju, Z. Zhao, Z. Zhang, W. Cong, et al., Ct super-resolution gan constrained by the identical, residual, and cycle learning ensemble (gan-circle), IEEE transactions on medical imaging 39 (1) (2019) 188–203

    work page 2019

  40. [40]

    Zhang, H

    K. Zhang, H. Hu, K. Philbrick, G. M. Conte, J. D. Sobek, P. Rouzrokh, B. J. Erickson, Soup-gan: Super-resolution mri using generative adversarial networks, Tomography 8 (2) (2022) 905–919. 21

    work page 2022

  41. [41]

    Saxena, J

    D. Saxena, J. Cao, Generative adversarial networks (gans) challenges, solutions, and future directions, ACM Computing Surveys (CSUR) 54 (3) (2021) 1–42

    work page 2021

  42. [42]

    J. Gui, Z. Sun, Y . Wen, D. Tao, J. Ye, A review on generative adversarial networks: Algorithms, theory, and applications, IEEE transactions on knowledge and data engineering 35 (4) (2021) 3313–3332

    work page 2021

  43. [43]

    Arjovsky, S

    M. Arjovsky, S. Chintala, L. Bottou, Wasserstein generative adversarial networks, in: International conference on machine learning, PMLR, 2017, pp. 214–223

    work page 2017

  44. [44]

    Mescheder, A

    L. Mescheder, A. Geiger, S. Nowozin, Which training methods for gans do actually converge?, in: International conference on machine learning, PMLR, 2018, pp. 3481–3490

    work page 2018

  45. [45]

    Y . Blau, T. Michaeli, The perception-distortion tradeoff, in: Proceedings of the IEEE conference on computer vision and pattern recognition, 2018, pp. 6228–6237

    work page 2018

  46. [46]

    Zhang, P

    R. Zhang, P. Isola, A. A. Efros, E. Shechtman, O. Wang, The unreasonable effectiveness of deep features as a perceptual metric, in: Proceed- ings of the IEEE conference on computer vision and pattern recognition, 2018, pp. 586–595

    work page 2018

  47. [47]

    Schollenberger, N

    J. Schollenberger, N. H. Osborne, L. Hernandez-Garcia, C. A. Figueroa, A combined computational fluid dynamics and arterial spin labeling mri modeling strategy to quantify patient-specific cerebral hemodynamics in cerebrovascular occlusive disease, Frontiers in Bioengineering and Biotechnology 9 (2021) 722445

    work page 2021

  48. [48]

    Ericsson, A

    L. Ericsson, A. Hjalmarsson, M. U. Akbar, E. Ferdian, M. Bonini, B. Hardy, J. Schollenberger, M. Aristova, P. Winter, N. Burris, et al., Generalized super-resolution 4d flow mri-using ensemble learning to extend across the cardiovascular system, IEEE journal of biomedical and health informatics (2024)

    work page 2024

  49. [49]

    C. J. Arthurs, R. Khlebnikov, A. Melville, M. Mar ˇcan, A. Gomez, D. Dillon-Murphy, F. Cuomo, M. Silva Vieira, J. Schollenberger, S. R. Lynch, et al., Crimson: An open-source software framework for cardiovascular integrated modelling and simulation, PLoS computational biology 17 (5) (2021) e1008881

    work page 2021

  50. [50]

    Schollenberger, D

    J. Schollenberger, D. J. Braet, L. Hernandez-Garcia, N. H. Osborne, C. A. Figueroa, A magnetic resonance imaging-based computational analysis of cerebral hemodynamics in patients with carotid artery stenosis, Quantitative Imaging in Medicine and Surgery 13 (2) (2023) 1126

    work page 2023

  51. [51]

    Schnell, S

    S. Schnell, S. Ansari, C. Wu, J. Garcia, I. Murphy, O. Rahman, A. Rahsepar, M. Aristova, J. Collins, J. Carr, Accelerated dual-venc 4d flow mri for neurovascular applications, Journal of Magnetic Resonance Imaging 46 (1) (2017) 102–114

    work page 2017

  52. [52]

    D. L. Parker, G. T. Gullberg, P. R. Frederick, Gibbs artifact removal in magnetic resonance imaging, Medical physics 14 (4) (1987) 640–645

    work page 1987

  53. [53]

    Gulrajani, F

    I. Gulrajani, F. Ahmed, M. Arjovsky, V . Dumoulin, A. C. Courville, Improved training of wasserstein gans, Advances in neural information processing systems 30 (2017)

    work page 2017

  54. [54]

    M. T. Islam, Z. Zhou, H. Ren, M. B. Khuzani, D. Kapp, J. Zou, L. Tian, J. C. Liao, L. Xing, Revealing hidden patterns in deep neural network feature space continuum via manifold learning, Nature Communications 14 (1) (2023) 8506

    work page 2023

  55. [55]

    Ahrens, B

    J. Ahrens, B. Geveci, C. Law, Paraview: An end-user tool for large-data visualization, in: C. D. Hansen, C. R. Johnson (Eds.), The Visualiza- tion Handbook, Elsevier, Oxford, UK, 2005, pp. 717–731

    work page 2005

  56. [56]

    Y . Xie, E. Franz, M. Chu, N. Thuerey, tempogan: A temporally coherent, volumetric gan for super-resolution fluid flow, ACM Transactions on Graphics (TOG) 37 (4) (2018) 1–15

    work page 2018

  57. [57]

    H. Kim, J. Kim, S. Won, C. Lee, Unsupervised deep learning for super-resolution reconstruction of turbulence, Journal of Fluid Mechanics 910 (2021) A29

    work page 2021

  58. [58]

    K. Xu, C. Li, J. Zhu, B. Zhang, Understanding and stabilizing gans’ training dynamics using control theory, in: International conference on machine learning, PMLR, 2020, pp. 10566–10575

    work page 2020

  59. [59]

    Heusel, H

    M. Heusel, H. Ramsauer, T. Unterthiner, B. Nessler, S. Hochreiter, Gans trained by a two time-scale update rule converge to a local nash equilibrium, Advances in neural information processing systems 30 (2017)

    work page 2017

  60. [60]

    Z. Chen, Y . Tong, Face super-resolution through wasserstein gans, arXiv preprint arXiv:1705.02438 (2017)

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  61. [61]

    Y . Tang, C. Liu, X. Zhang, Single image super-resolution using wasserstein generative adversarial network with gradient penalty, Pattern Recognition Letters 163 (2022) 32–39

    work page 2022

  62. [62]

    M. Ran, J. Hu, Y . Chen, H. Chen, H. Sun, J. Zhou, Y . Zhang, Denoising of 3d magnetic resonance images using a residual encoder–decoder wasserstein generative adversarial network, Medical image analysis 55 (2019) 165–180

    work page 2019

  63. [63]

    Jiang, Z

    M. Jiang, Z. Yuan, X. Yang, J. Zhang, Y . Gong, L. Xia, T. Li, Accelerating cs-mri reconstruction with fine-tuning wasserstein generative adversarial network, IEEE Access 7 (2019) 152347–152357

    work page 2019

  64. [64]

    M. Zhao, Y . Wei, K. K. Wong, A generative adversarial network technique for high-quality super-resolution reconstruction of cardiac magnetic resonance images, Magnetic resonance imaging 85 (2022) 153–160

    work page 2022

  65. [65]

    M. A. Morales, F. Ghanbari, ¨O. B. Demirel, J. A. Street, T. E. Wallace, R. Davids, J. Rodriguez, S. Johnson, P. Pierce, W. J. Manning, et al., Accelerated phase-contrast magnetic resonance imaging with use of resolution enhancement generative adversarial neural network, Journal of Cardiovascular Magnetic Resonance 27 (1) (2025) 101128

    work page 2025

  66. [66]

    N. M. Patel, E. R. Bartusiak, S. M. Rothenberger, A. Schwichtenberg, E. J. Delp, V . L. Rayz, A. D. N. Initiative, Super-resolving and denoising 4d flow mri of neurofluids using physics-guided neural networks, Annals of Biomedical Engineering 53 (2) (2025) 331–347

    work page 2025

  67. [67]

    Kissas, Y

    G. Kissas, Y . Yang, E. Hwuang, W. R. Witschey, J. A. Detre, P. Perdikaris, Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4d flow mri data using physics-informed neural networks, Computer Methods in Applied Mechanics and Engineering 358 (2020) 112623

    work page 2020

  68. [68]

    Shone, N

    F. Shone, N. Ravikumar, T. Lassila, M. MacRaild, Y . Wang, Z. A. Taylor, P. Jimack, E. Dall’Armellina, A. F. Frangi, Deep physics-informed super-resolution of cardiac 4d-flow mri, in: International Conference on Information Processing in Medical Imaging, Springer, 2023, pp. 511–522

    work page 2023

  69. [69]

    Sautory, S

    T. Sautory, S. C. Shadden, Unsupervised denoising and super-resolution of vascular flow data by physics-informed machine learning, Journal of Biomechanical Engineering 146 (9) (2024)

    work page 2024

  70. [70]

    Gormezano, S

    C. Gormezano, S. Shadden, Denoising and super-resolution of flow data by physics-informed markov random fields, in: APS Division of Fluid Dynamics Meeting Abstracts, 2024, pp. J15–003

    work page 2024

  71. [71]

    Catapano, G

    F. Catapano, G. Pambianchi, G. Cundari, J. Rebelo, F. Cilia, I. Carbone, C. Catalano, M. Francone, N. Galea, 4d flow imaging of the thoracic 22 aorta: is there an added clinical value?, Cardiovascular Diagnosis and Therapy 10 (4) (2020) 1068

    work page 2020

  72. [72]

    Demirkiran, P

    A. Demirkiran, P. van Ooij, J. J. Westenberg, M. B. Hofman, H. C. van Assen, L. J. Schoonmade, U. Asim, C. P. Blanken, A. J. Ned- erveen, A. C. van Rossum, et al., Clinical intra-cardiac 4d flow cmr: acquisition, analysis, and clinical applications, European Heart Journal- Cardiovascular Imaging 23 (2) (2022) 154–165

    work page 2022

  73. [73]

    Knapp, M

    J. Knapp, M. Tavares de Sousa, A. Lenz, J. Herrmann, S. Zhang, F. Kording, B. Hergert, G. Adam, P. Bannas, B. Schoennagel, Fetal 4d flow mri of the great thoracic vessels at 3 tesla using doppler-ultrasound gating: a feasibility study, European radiology 33 (3) (2023) 1698–1706

    work page 2023

  74. [74]

    Yamada, H

    S. Yamada, H. Ito, M. Ishikawa, K. Yamamoto, M. Yamaguchi, M. Oshima, K. Nozaki, Quantification of oscillatory shear stress from reciprocating csf motion on 4d flow imaging, American journal of neuroradiology 42 (3) (2021) 479–486

    work page 2021

  75. [75]

    Takehara, 4d flow when and how?, La radiologia medica 125 (9) (2020) 838–850

    Y . Takehara, 4d flow when and how?, La radiologia medica 125 (9) (2020) 838–850

    work page 2020

  76. [76]

    Callmer, M

    P. Callmer, M. Bonini, E. Ferdian, D. Nordsletten, D. Giese, A. A. Young, A. Fyrdahl, D. Marlevi, Deep learning for temporal super-resolution 4d flow mri, arXiv preprint arXiv:2501.08780 (2025). 23

    work page arXiv 2025