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REVIEW 3 major objections 5 minor 29 references

Sparsity-Driven Parallel Imaging Consistency for Improved Self-Supervised MRI Reconstruction

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Adding a sparse parallel-imaging consistency term to self-supervised training lets MRI reconstruction networks suppress aliasing and noise at acceleration factors 6 and 8 without fully-sampled references.

desk verdict A genuinely new self-supervised training loss for MRI reconstruction, but the paper's own Table 1 contradicts the 'consistently outperforms' claim and the core linearity assumption is untested. read the letter →

arxiv 2505.24136 v1 pith:QGKPW5IK submitted 2025-05-30 eess.IV cs.AIcs.CVcs.LGphysics.med-ph

Yaşar Utku Alçalar , Mehmet Akçakaya This is my paper
classification eess.IVcs.AIcs.CVcs.LGphysics.med-ph
keywords self-supervisedMRIreconstructionparallelimagingsparse-domainconsistencydataundersamplingphysics-drivendeeplearningaliasingartifactsdual-treecomplexwavelettransformhighaccelerationrates
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper proposes a way to train MRI reconstruction networks when no fully-sampled reference images are available, by adding a consistency term to the standard multi-mask self-supervised loss. The term feeds the network the same frequency-domain (k-space) data with and without a small designed perturbation and trains the difference of the two outputs to match the true perturbation in a sparse wavelet domain. On knee and brain MRI data undersampled at acceleration factors 6 and 8, the authors report that this term reduces aliasing artifacts and noise more effectively than three prior self-supervised and unsupervised methods, bringing quality close to supervised training. If it holds up, the method would make higher acceleration factors practical in clinical MRI without the usual loss of fidelity.

What carries the argument

The load-bearing object is the sparse parallel imaging consistency term $\mathcal{L}_{\mathrm{spic}}$ (Eq. 8), computed as the reweighted $\ell^1$ distance between the true perturbation $p$ and the network's predicted perturbation $p_{\mathrm{est}} = f(y_\Omega+q_\Omega,E_\Omega;\theta)-f(y_\Omega,E_\Omega;\theta)$, after applying the dual-tree complex wavelet transform (a shift-sensitive multi-scale transform that sparsifies MR images) as the sparsifying operator $W$ and normalizing by $|(Wp_{\mathrm{true}})_n|+\epsilon$. The perturbations are designed so that, at acceleration rate $R$, their aliased copies do not fold over one another, making them recoverable by parallel imaging; the sparse-domain weighting follows reweighted $\ell^1$ minimization. The role of this term is to couple the network's behavior to classical parallel-imaging consistency during training, which is what the paper credits for artifact and noise suppression at high acceleration.

What would settle it

Train the same PD-DL network on the same knee data with and without the sparse consistency term (Eq. 8), holding all other settings fixed, and compare test PSNR and SSIM at acceleration rate 8; if the difference is within the run-to-run variability of the self-supervised baselines, the central claim would be undercut, since the paper attributes its gains specifically to this term.

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Extended reading notes

Core claim

The central claim is that a sparsity-driven parallel imaging consistency term, appended to the MM-SSDU objective, is what lets a self-supervised physics-driven deep learning network suppress coherent aliasing and noise at high acceleration. The paper defines perturbations $p$ whose undersampled k-space signatures $q_\Omega = E_\Omega p$ alias without overlapping in the field of view, so a parallel-imaging reconstruction can in principle recover them. It then asserts that a well-trained network should satisfy $p = f(y_\Omega+q_\Omega,E_\Omega;\theta)-f(y_\Omega,E_\Omega;\theta)$, and enforces the estimated perturbation in a dual-tree complex wavelet domain with a reweighted $\ell^1$ loss. The result, SPIC-SSDU, is reported to achieve the best PSNR and SSIM among MM-SSDU, ULIM, and CC-SSDU on coronal PD, coronal PD-FS knee, and axial T2 brain data at acceleration rates 6 and 8, approaching supervised learning and even removing some residual artifacts seen in supervised reconstructions.

Load-bearing premise

The training signal assumes that adding a designed perturbation to the network's input shifts the network's output by exactly that perturbation, even though the network is a nonlinear learned map; if this does not hold, the consistency term enforces a relation that may not be true.

Editorial extensions

If this is right

  • SPIC-SSDU outperforms MM-SSDU, ULIM, and CC-SSDU in PSNR and SSIM on all three tested datasets at both acceleration rates 6 and 8.
  • Sparse-domain perturbation consistency beats a plain $\ell^2$ spatial-domain perturbation loss, yielding sharper images with fewer artifacts.
  • Self-supervised training with SPIC-SSDU approaches supervised reconstruction quality, and in some cases removes residual aliasing that supervised training leaves behind.
  • The same framework is claimed to be applicable to random Cartesian and radial undersampling patterns, though only equidistant sampling is evaluated.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper does not test the additivity assumption behind Eq. (7); measuring $p_{\mathrm{est}}$ against $p_{\mathrm{true}}$ for a range of inputs would show how much bias this introduces.
  • Because the sparse consistency term targets a different failure mode than cyclic-consistency methods, it could plausibly be combined with them for further gains, a combination the paper does not explore.
  • The perturbation design is tailored to coherent, equidistant undersampling, so the largest benefits would be expected in that clinically relevant setting; random undersampling may show smaller improvements.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript proposes SPIC-SSDU, a self-supervised training scheme for physics-driven deep learning (PD-DL) MRI reconstruction. It augments the MM-SSDU loss with a sparse-domain consistency term computed by adding designed perturbations to the measured k-space data and comparing the network's response difference against the true perturbation in the dual-tree complex wavelet domain with a reweighted L1 loss. Experiments on fastMRI knee and brain datasets at R=6 and R=8 with equispaced undersampling compare the method with supervised learning, MM-SSDU, ULIM, and CC-SSDU using PSNR/SSIM and example images. The paper claims consistent artifact and noise reduction and quantitative improvements over the unsupervised/self-supervised baselines.

Significance. The proposed idea of adding a sparse-domain parallel-imaging consistency term to MM-SSDU is interesting and, if validated, could improve self-supervised reconstruction at high acceleration factors. Strengths include the use of public fastMRI knee and brain data, comparison against three relevant baselines, and use of the same network architecture for all methods. However, the quantitative support for the central claim is currently weak: the reported improvements are small, the PSNR result is not consistent across all settings, and the key assumption behind Eq. (7) is not tested. The contribution is therefore a promising incremental method that needs further validation before it can be assessed as a reliable improvement.

major comments (3)
  1. [Section 4.3 / Table 1] The claim that SPIC-SSDU 'consistently outperforms other unsupervised and self-supervised methods in terms of PSNR and SSIM values' is contradicted by the reported numbers: on coronal PD at R=8, CC-SSDU has PSNR 35.76 versus 35.64 for SPIC-SSDU, and on axial T2 at R=6, MM-SSDU has PSNR 35.32 versus 35.24 for SPIC-SSDU. Moreover, the favorable differences when SPIC-SSDU does lead are often 0.01-0.05 dB, and no error bars, confidence intervals, or significance tests are reported. Please revise the claim, add per-slice or repeated-run statistics, or both.
  2. [Section 3, Eq. (7)] The definition of the sparse parallel-imaging consistency term in Eq. (8) relies on the equality p = f(y+q, E; theta) - f(y, E; theta) stated in Eq. (7). This equality is exact for a linear reconstruction operator that is a right inverse of the encoding operator, but the unrolled PD-DL network is nonlinear due to the CNN regularizer, and the paper provides neither a theoretical argument nor an empirical test that the equality holds approximately for the chosen perturbations. Because the entire proposed loss is built on this relation, this assumption is load-bearing. Please provide such a validation, e.g., measuring the residual f(y+q)-f(y)-p on validation data for the actual trained models.
  3. [Section 4.1] The construction of the perturbations p_k is not specified. The text says '3 perturbations with 3 k-space masks' and describes them only as 'well-designed perturbations' that prevent fold-overs, but it does not state how each perturbation is generated, how it is paired with a mask, or how the design guarantees recoverability by parallel imaging. Without this information the method cannot be reproduced and the validity of Eq. (7) cannot be assessed. Please provide the explicit construction algorithm.
minor comments (5)
  1. [Section 4.3] The sentence that SPIC-SSDU achieves performance 'matching supervised learning' while reducing its artifacts at R=6 across all datasets is not supported by Table 1, since supervised learning has higher PSNR than SPIC-SSDU on coronal PD-FS at R=6 (34.45 vs. 34.05) and on axial T2 at R=6 (35.42 vs. 35.24). Please qualify this statement.
  2. [Section 4.1] The choice beta = 5e-3 and the number of perturbations/masks are reported without a sensitivity study; given the importance of the trade-off between the MM-SSDU term and the sparse PIC term, a small hyperparameter sweep would strengthen the paper.
  3. [Section 4.2] The paper does not report the hyperparameters used for the ULIM and CC-SSDU baselines beyond their loss formulations; for a fair and reproducible comparison, state whether all methods used the same training schedule, loss weighting, and mask settings.
  4. [Figure 4] Figure 4 demonstrates the benefit of the sparse-domain loss over the L2 spatial-domain loss with a single qualitative example; provide quantitative metrics or a small dataset-wide comparison to support this claim.
  5. [Throughout] There are minor typographical errors: 'A schmeatic' (Section 2.2) should be 'A schematic', and 'demonstrates slights artifacts' (Section 4.3) should be 'demonstrates slight artifacts'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the sparse perturbation consistency loss uses known perturbations as its own self-supervised target, and the same-group baseline citations are not load-bearing.

full rationale

The central loss (Eq. 9) is the MM-SSDU expectation loss plus a sparse parallel-imaging consistency term (Eq. 8). The consistency term computes p_est = f(y+q,E;θ)−f(y,E;θ) and compares it, in a weighted ℓ1 sense, with the known perturbation p. Although p_true is known by construction, this is exactly what a self-supervised auxiliary task is supposed to do; it is not a fitted parameter being relabeled as a prediction. Eq. (7), p = f(y+q,E;θ)−f(y,E;θ), is an assumption about the network's perturbation-recovery behavior, not a relation derived from the forward model or from the final loss; if the unrolled network is nonlinear the assumption may fail, but that is a modeling risk, not circularity. The quantitative claims rest on empirical comparisons to MM-SSDU, ULIM, and CC-SSDU on fastMRI data; the two same-group baselines (MM-SSDU and CC-SSDU) are previously published methods and are not used to justify the new consistency term. The only borrowed prescriptions (ρ=0.4 from [7] and reweighted ℓ1 from [20]) are standard external choices. No step in the derivation reduces by construction to its own input.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The method introduces no new physical entities. Its load-bearing assumptions are the linearity of the network with respect to perturbations (Eq. 7), the recoverability of designed perturbations, and the choice of hyperparameters such as beta. These are domain assumptions rather than derived results.

free parameters (4)
  • beta (trade-off parameter) = 5e-3
    Weights the sparse parallel imaging consistency term against the MM-SSDU loss in Eq. (9). Chosen without sensitivity analysis or a principled selection procedure (Section 4.1).
  • epsilon (stability constant) = not specified
    Used in the denominator of Eq. (8) to avoid division by zero. The value is not reported, but it affects the loss magnitude.
  • number of perturbations and masks = 3 perturbations, 3 masks
    Chosen empirically; no ablation on this number is provided (Section 4.1).
  • rho = |Lambda|/|Theta| = 0.4
    Split ratio for self-supervised masks, taken as recommended from prior work [7] without re-tuning for this method.
assumptions (4)
  • domain assumption The PD-DL reconstruction operator satisfies the additivity/linearity assumption p = f(y+q,E) - f(y,E) in Eq. (7).
    The entire consistency loss is built on this relation, but the paper provides no justification or empirical check for it. A nonlinear network may violate this, making the loss biased. Stated in Section 3, Eq. (7).
  • domain assumption The designed perturbations are recoverable by parallel imaging (SENSE) because they avoid aliasing overlap, as stated in Section 3.
    The paper asserts this property but gives no formal proof or algorithm for constructing such perturbations, only a qualitative description.
  • standard math Reweighted l1 minimization (Candes et al. [20]) improves sparsity and is beneficial for this consistency term.
    The paper adopts reweighted l1 weighting without demonstrating its advantage over other sparsity-promoting losses in this specific context, beyond a visual ablation in Fig. 4.
  • domain assumption Equispaced undersampling with 24 central k-space lines is representative of clinical practice for the claims made.
    The method is evaluated only on this sampling pattern, yet the discussion claims generalizability to random and radial undersampling without supporting experiments.

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Cite this review

Pith. "Pith review of Sparsity-Driven Parallel Imaging Consistency for Improved Self-Supervised MRI Reconstruction." pith.science (2026). https://pith.science/paper/QGKPW5IK

@misc{pith2026250524136,
  author       = {Pith},
  title        = {Pith review of: Sparsity-Driven Parallel Imaging Consistency for Improved Self-Supervised MRI Reconstruction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QGKPW5IK}},
  note         = {Machine review of arXiv:2505.24136}
}
read the original abstract

Physics-driven deep learning (PD-DL) models have proven to be a powerful approach for improved reconstruction of rapid MRI scans. In order to train these models in scenarios where fully-sampled reference data is unavailable, self-supervised learning has gained prominence. However, its application at high acceleration rates frequently introduces artifacts, compromising image fidelity. To mitigate this shortcoming, we propose a novel way to train PD-DL networks via carefully-designed perturbations. In particular, we enhance the k-space masking idea of conventional self-supervised learning with a novel consistency term that assesses the model's ability to accurately predict the added perturbations in a sparse domain, leading to more reliable and artifact-free reconstructions. The results obtained from the fastMRI knee and brain datasets show that the proposed training strategy effectively reduces aliasing artifacts and mitigates noise amplification at high acceleration rates, outperforming state-of-the-art self-supervised methods both visually and quantitatively.

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Works this paper leans on

29 extracted references · 28 canonical work pages

  1. [1]

    Physics-driven deep learning (PD-DL) models have emerged as a powerful solution to accelerate MRI while preserving im- age quality [1–5]

    INTRODUCTION Magnetic resonance imaging (MRI) is a vital tool in mod- ern radiology, but its long acquisition times pose challenges. Physics-driven deep learning (PD-DL) models have emerged as a powerful solution to accelerate MRI while preserving im- age quality [1–5]. Traditional supervised learning approaches require fully-sampled k-space data [1–3,6],...

    work page 2025

  2. [2]

    BACKGROUND AND RELA TED WORK 2.1. MRI Inverse Problem and PD-DL Unrolling The MRI forward model that relates the underlying image x to the acquired k-space data yΩ is given as: yΩ = EΩx + n, (1) where Ω is the k-space undersampling pattern, EΩ is the multi-coil encoding operator that incorporates partial Fourier sampling, coil sensitivities, and the under...

    work page Pith review arXiv 2025

  3. [3]

    Our key innovation involves augmenting the MM-SSDU loss, as defined in (4), with a novel consistency term, which we refer to as sparse parallel imaging consistency

    SELF-SUPERVISION VIA SPARSITY-DRIVEN PARALLEL IMAGING CONSISTENCY In this work, we take inspiration from classical MR recon- struction techniques, such as parallel imaging [15, 17] and compressed sensing [19], to introduce a novel self-supervised framework for training PD-DL networks, enabling high- quality reconstructions even at very high acceleration r...

    work page

  4. [4]

    Imaging Experiments and Implementation Details We conducted a comprehensive evaluation of our method with both qualitative and quantitative assessments

    EV ALUA TIONS 4.1. Imaging Experiments and Implementation Details We conducted a comprehensive evaluation of our method with both qualitative and quantitative assessments. Fully-sampled multi-coil knee and brain MRI data from the New York Uni- versity (NYU) fastMRI database [13] were used. The knee dataset comprised of fully-sampled coronal proton density...

    work page

  5. [5]

    DISCUSSION AND CONCLUSION In this study, we introduce SPIC-SSDU, a novel framework that combines concepts from parallel imaging and com- pressed sensing to improve self-supervised PD-DL MRI reconstruction, particularly at high acceleration rates. By augmenting the MM-SSDU loss with a sparse parallel imag- ing consistency term, we ensure better alignment b...

    work page

  6. [6]

    ACKNOWLEDGMENTS This work was partially supported by NIH R01HL153146, NIH R01EB032830, NIH P41EB027061

    work page

  7. [7]

    A deep cascade of convolutional neural networks for dynamic MR image reconstruction,

    J. Schlemper, J. Caballero, J. V . Hajnal, A. N. Price, and D. Rueckert, “A deep cascade of convolutional neural networks for dynamic MR image reconstruction,” IEEE Trans. Med. Imag., vol. 37, no. 2, pp. 491–503, 2018

    work page 2018

  8. [8]

    Learning a vari- ational network for reconstruction of accelerated MRI data,

    K. Hammernik, T. Klatzer, E. Kobler, M. P. Recht, D. K. Sodickson, T. Pock, and F. Knoll, “Learning a vari- ational network for reconstruction of accelerated MRI data,” Magn. Reson. Med. , vol. 79, no. 6, pp. 3055– 3071, 2018

    work page 2018

Show all 29 references
  1. [9]

    MoDL: Model-based deep learning architecture for inverse problems,

    H. K. Aggarwal, M. P. Mani, and M. Jacob, “MoDL: Model-based deep learning architecture for inverse problems,” IEEE Trans. Med. Imag. , vol. 38, no. 2, pp. 394–405, 2019

    2019

  2. [10]

    Convolutional recurrent neural networks for dynamic MR image reconstruction,

    C. Qin, J. Schlemper, J. Caballero, A. N. Price, J. V . Ha- jnal, and D. Rueckert, “Convolutional recurrent neural networks for dynamic MR image reconstruction,” IEEE Trans. Med. Imag., vol. 38, no. 1, pp. 280–290, 2019

    2019

  3. [11]

    ADMM-CSNet: A deep learning approach for image compressive sensing,

    Y . Yang, J. Sun, H. Li, and Z. Xu, “ADMM-CSNet: A deep learning approach for image compressive sensing,” IEEE Trans. Pattern Anal. Mach. Intell. , vol. 42, no. 3, pp. 521–538, Mar. 2020

    2020

  4. [12]

    Neural proximal gra- dient descent for compressive imaging,

    M. Mardani, Q. Sun, D. Donoho, V . Papyan, H. Mona- jemi, S. Vasanawala, and J. Pauly, “Neural proximal gra- dient descent for compressive imaging,” in Proc. Adv. Neural Inf. Process. Syst., 2018, vol. 31

    2018

  5. [13]

    Multi-mask self-supervised learning for physics-guided neural networks in highly accelerated magnetic resonance imaging,

    B. Yaman, H. Gu, S. A. H. Hosseini, ¨O. B. Demirel, S. Moeller, J. Ellermann, K. U ˘gurbil, and M. Akc ¸akaya, “Multi-mask self-supervised learning for physics-guided neural networks in highly accelerated magnetic resonance imaging,” NMR Biomed. , vol. 35, no. 12, 2022, Art. no. e4798

    2022

  6. [14]

    Equivariant imaging: Learning beyond the range space,

    D. Chen, J. Tachella, and M. E. Davies, “Equivariant imaging: Learning beyond the range space,” in Proc. IEEE/CVF Int. Conf. Comput. Vis. , 2021, pp. 4379– 4388

    2021

  7. [15]

    Robust compressed sensing MRI with deep generative priors,

    A. Jalal, M. Arvinte, G. Daras, E. Price, A. G. Dimakis, and J. Tamir, “Robust compressed sensing MRI with deep generative priors,” in Proc. Adv. Neural Inf. Pro- cess. Syst., 2021, pp. 14938–14954

    2021

  8. [16]

    Score-based diffusion models for accelerated MRI,

    H. Chung and J. C. Ye, “Score-based diffusion models for accelerated MRI,” Med. Image Anal., vol. 80, 2022, Art. no. 102479

    2022

  9. [17]

    Cycle- consistent self-supervised learning for improved highly- accelerated MRI reconstruction,

    C. Zhang, O. B. Demirel, and M. Akc ¸akaya, “Cycle- consistent self-supervised learning for improved highly- accelerated MRI reconstruction,” in Proc. IEEE Int. Symp. Biomed. Imag., 2024, pp. 1–5

    2024

  10. [18]

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

    C. Millard and M. Chiew, “A theoretical framework for self-supervised MR image reconstruction using sub- sampling via variable density Noisier2Noise,” IEEE Trans. Comput. Imag., vol. 9, pp. 707–720, 2023

    2023

  11. [19]

    fastMRI: A publicly available raw k-space and DICOM dataset of knee im- ages for accelerated MR image reconstruction using ma- chine learning,

    F. Knoll, J. Zbontar, A. Sriram, M. J. Muckley, M. Bruno, A. Defazio, M. Parente, K. J. Geras, J. Kat- snelson, H. Chandarana, et al., “fastMRI: A publicly available raw k-space and DICOM dataset of knee im- ages for accelerated MR image reconstruction using ma- chine learning...

    2020

  12. [20]

    Unsuper- vised learning from incomplete measurements for in- verse problems,

    J. Tachella, D. Chen, and M. Davies, “Unsuper- vised learning from incomplete measurements for in- verse problems,” inProc. Adv. Neural Inf. Process. Syst., 2022, pp. 4983–4995

    2022

  13. [21]

    SENSE: Sensitivity encoding for fast MRI,

    K. P. Pruessmann, M. Weiger, M. B. Scheidegger, and P. Boesiger, “SENSE: Sensitivity encoding for fast MRI,” Magn. Reson. Med., vol. 42, no. 5, pp. 952–962, 1999

    1999

  14. [22]

    Advances in sensitivity encoding with arbitrary k-space trajectories,

    K. P. Pruessmann, M. Weiger, P. B ¨ornert, and P. Boe- siger, “Advances in sensitivity encoding with arbitrary k-space trajectories,” Magn. Reson. Med., vol. 46, no. 4, pp. 638–651, 2001

    2001

  15. [23]

    Gen- eralized autocalibrating partially parallel acquisitions (GRAPPA),

    M. A. Griswold, P. M. Jakob, R. M. Heidemann, M. Nit- tka, V . Jellus, J. Wang, B. Kiefer, and A. Haase, “Gen- eralized autocalibrating partially parallel acquisitions (GRAPPA),” Magn. Reson. Med. , vol. 47, no. 6, pp. 1202–1210, 2002

    2002

  16. [24]

    Optimization methods for magnetic res- onance image reconstruction,

    J. A. Fessler, “Optimization methods for magnetic res- onance image reconstruction,” IEEE Signal Process. Mag., vol. 37, no. 1, pp. 33–40, 2020

    2020

  17. [25]

    Sparse MRI: The application of compressed sensing for rapid MR imaging,

    M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med., vol. 58, no. 6, pp. 1182– 1195, Dec. 2007

    2007

  18. [26]

    Enhanc- ing sparsity by reweighted ℓ1 minimization,

    E. J. Cand `es, M. B. Wakin, and S. P. Boyd, “Enhanc- ing sparsity by reweighted ℓ1 minimization,” J. F ourier Anal. Appl., vol. 14, no. 5, pp. 877–905, 2008

    2008

  19. [27]

    Assessment of the gen- eralization of learned image reconstruction and the po- tential for transfer learning,

    F. Knoll, K. Hammernik, E. Kobler, T. Pock, M. P. Recht, and D. K. Sodickson, “Assessment of the gen- eralization of learned image reconstruction and the po- tential for transfer learning,” Magn. Reson. Med. , vol. 81, no. 1, pp. 116–128, 2019

    2019

  20. [28]

    NTIRE 2017 challenge on single im- age super-resolution: Methods and results,

    R. Timofte, E. Agustsson, L. V . Gool, M.-H. Yang, and L. Zhang, “NTIRE 2017 challenge on single im- age super-resolution: Methods and results,” in Proc. IEEE/CVF Conf. Comput. Vis. Pattern Recog. Worksh. , 2017, pp. 114–125

    2017

  21. [29]

    The dual-tree complex wavelet transform,

    I. W. Selesnick, R. G. Baraniuk, and N. C. Kingsbury, “The dual-tree complex wavelet transform,” IEEE Sig- nal Process. Mag., vol. 22, no. 6, pp. 123–151, 2005

    2005

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