Pith. sign in

REVIEW 4 major objections 5 minor 41 references

An unsupervised method for MRI recovery: Deep image prior with structured sparsity

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read DISCUS: one untrained U-Net with group-sparse dynamic codes reconstructs free-breathing cardiac MRI without fully sampled training data, and the number of nonzero code entries reports the data's manifold dimension.

desk verdict DISCUS is a solid, practically useful extension of DIP for dynamic MRI, but the manifold-discovery claim is not supported by the evidence. read the letter →

arxiv 2501.01482 v3 pith:WVX6T32Q submitted 2025-01-02 eess.IV cs.CVcs.LGeess.SP

Muhammad Ahmad Sultan , Chong Chen , Yingmin Liu , Katarzyna Gil , Karolina Zareba , Rizwan Ahmad This is my paper · ORCID
classification eess.IVcs.CVcs.LGeess.SP
keywords unsupervisedMRIreconstructiondeepimagepriorgroupsparsitymanifoldlearninglategadoliniumenhancementdynamicsingle-shotcardiacimagingstructured
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 DISCUS, an unsupervised method for reconstructing dynamic MRI series that does not need fully sampled k-space data for training. The central claim is that a single U-Net, fed one static code vector and one per-frame dynamic code vector, can generate every frame of a free-breathing late gadolinium enhancement (LGE) series, provided the dynamic codes are penalized with group sparsity. That penalty makes the nonzero entries of the learned codes shared across frames, so the number of surviving entries reports the true dimensionality of the image manifold without the user having to preset it. The paper reports that DISCUS outperforms compressed sensing, low-rank plus sparse, deep image prior, and self-guided deep image prior on simulated phantoms, simulated LGE series, retrospectively undersampled patient data, and prospectively undersampled patient data scored by expert readers. If the claim holds, dynamic MRI reconstruction becomes feasible in settings where fully sampled references do not exist and the number of motion and contrast degrees of freedom is unknown.

What carries the argument

The load-bearing mechanism is the hybrid $\ell_2$-$\ell_1$ group-sparsity regularizer applied to the dynamic code vectors. A U-Net $G_\theta$ maps the concatenation of a static code $z_0$ (three channels in the implementation) and a single-channel dynamic code $z_t$ to an estimate of frame $x_t$; the regularizer computes $\|z_{(1:T)}\|_{2,1} = \sum_{n=1}^{N} \sqrt{\sum_{t=1}^{T} z_t[n]^2}$, which penalizes the temporal energy of each pixel and forces the nonzero entries of $z_t$ to occupy the same positions across all frames. Counting those surviving positions after training gives the dimension of the image manifold, and the values of the surviving entries encode frame-to-frame variation. This distinguishes DISCUS from plain deep image prior, which has no code sparsity and is prone to overfitting, and from manifold methods that fix the dimension in advance or enforce temporal smoothness.

What would settle it

Run DISCUS on a digital phantom with a known, larger number of independent motion modes, say five local deformations with disjoint spatial supports, and compare the post-training support count with the true number across ten random restarts; the central claim would fail if the method regularly undercounts or overcounts, because the shared-support representation then cannot capture the true dynamics. A second check uses the paper's own two-motion phantom, where two of ten restarts estimated three dimensions, and asks whether those wrong-dimension runs also produce visibly incorrect reconstructions.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that structured sparsity in latent space turns an untrained convolutional network into a manifold learner. DISCUS solves the objective in Equation (3): minimize $\sum_{t}\|A_t G_\theta(z_0, z_t) - y_t\|_2^2 + \lambda \|z_{(1:T)}\|_{2,1}$ over the network weights $\theta$, a static code $z_0$, and dynamic codes $z_t$, where the $\ell_{2,1}$ term first takes per-pixel energy across time and then sums over pixels. Because this hybrid norm drives entire pixels' temporal trajectories to zero together, the learned dynamic codes share a common support; the number of nonzero entries in the trained $\hat{z}_t$ is the discovered manifold dimension. The paper claims this support count matched the true dimension in the dynamic-phantom study (one for pure rotations, one for pure translations, and two for the combined motion in eight of ten runs) and that the resulting joint reconstruction outperformed compressed sensing, low-rank plus sparse, DIP, and SG-DIP in NMSE and SSIM across acceleration rates, with DISCUS being chosen as best most often in the prospective expert study. The method does not assume nearby frames are similar, which is why the authors position it for single-shot free-breathing LGE rather than for cine.

Load-bearing premise

The load-bearing premise is that every frame-to-frame change in the image series can be represented by a small set of code entries whose positions are shared across frames; if real motion or contrast changes need many independent degrees of freedom, the group-sparsity penalty will either erase them or lock onto the wrong support.

Editorial extensions

If this is right

  • Free-breathing single-shot LGE series can be reconstructed without fully sampled training data, without a preset manifold dimension, and without assuming temporally close frames look alike.
  • The ablation results imply that most of the quality gain comes from group sparsity: the no-group-sparsity variant trails DISCUS by more than 3 dB at every tested frame count.
  • Larger numbers of frames improve DISCUS quality, so the method exploits shared information across the whole series rather than reconstructing each frame independently.
  • The same framework is positioned to carry over to other single-shot dynamic applications such as first-pass perfusion and parametric mapping, where consecutive frames are not necessarily similar and fully sampled references are hard to obtain.

Reading between the lines

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

  • The paper's own dynamic-phantom result, where two of ten restarts found three nonzero entries instead of two, suggests that the discovered dimension should be treated as a distribution over restarts rather than a single exact number in practice.
  • Because the $\ell_{2,1}$ penalty does not depend on the sampling trajectory, DISCUS should extend to radial or spiral single-shot acquisitions without changing the objective; the paper only tests Cartesian GRO masks.
  • A clinically useful extension would be to correlate the discovered manifold dimension with independent recordings of respiratory and cardiac motion; if the count tracks the number of physiological drivers, DISCUS could double as a motion-characterization tool.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper proposes DISCUS, an unsupervised dynamic MRI reconstruction method that extends deep image prior by adding group sparsity to frame-specific code vectors (Eq. 3). A single U-Net maps one static code z0 and one dynamic code zt to each frame, and the ℓ2,1 penalty on z(1:T) is intended to force the dynamic codes to share a small support, whose size the authors equate with the intrinsic dimensionality of the image manifold. The method is evaluated in four studies: a Shepp-Logan phantom with known manifold dimension (Study I), simulated free-breathing LGE from digital phantoms (Study II), retrospectively undersampled patient LGE (Study III), and prospectively undersampled patient LGE with blinded expert scoring (Study IV). DISCUS is compared against CS, L+S, DIP, and SG-DIP. The authors report consistently better NMSE/SSIM and expert scores, and they release code and representative data.

Significance. If the results hold, DISCUS would be a practically useful unsupervised reconstruction method for dynamic MRI because it requires no fully sampled training data and no pre-specified manifold dimension. The paper has genuine strengths: four complementary studies, an ablation isolating the group-sparsity contribution, blinded expert evaluation on prospective data, and public code/data. However, the central conceptual claim—that the support size of the learned dynamic codes measures the true manifold dimensionality—is not established, because the objective itself penalizes support and no threshold for 'nonzero' is given. The reconstruction-quality comparisons are convincing within the chosen baseline set, but the absence of manifold-based baselines and the small prospective reader study limit the strength of the broader claims. The manuscript is technically sound enough to merit revision, but the central claim needs reframing or additional evidence.

major comments (4)
  1. [Section 2.2, Eq. (3), Section 3.1] The statement that 'the number of non-zero entries in bz_t determines the dimensionality of the underlying manifold' is not supported as a discovery claim. The objective in Eq. (3) directly penalizes the temporal support of z(1:T) through the ℓ2,1 term, so finding few active entries is partly a regularization outcome, not an independent measurement. Moreover, Adam does not return exact zeros, yet no threshold for 'nonzero' is specified anywhere in Sections 2.3 or 3.1. Because Gθ is a nonlinear U-Net with spatial mixing, the support size in code space is not invariant to reparameterization: one active code pixel can affect many output degrees of freedom, and multiple active pixels can be redundant. Study I only achieves 8/10 correct dimensionality for the two-dimensional manifold, and the paper itself notes that the two active entries did not disentangle rotation from translation. I recommend reframing the contribution as 'DISCUS imposes a low-dimensional shared-support representation' rather than 'DISCUS discovers the manifold dimension,' and, if the discovery claim is retained, providing a precise zero-threshold definition, an invariance analysis, and a validation on real LGE data with an independent dimension estimate.
  2. [Section 2.8 and Section 3 (Studies II-IV)] The paper positions DISCUS against manifold-based dynamic DIP methods such as those of Yoo et al. and Gen-SToRM, and it claims superior performance, but no manifold-based baseline (e.g., time-dependent DIP, Gen-SToRM, DEBLUR, or MoCo-SToRM) is included in the comparisons. The current baselines (CS, L+S, DIP, SG-DIP) are reasonable but do not test the specific advantage DISCUS claims over methods that explicitly model a low-dimensional manifold. I ask the authors to either add at least one manifold-based baseline to the numerical comparisons or soften the comparative claims so that they are restricted to the evaluated methods.
  3. [Section 2.6 and Table 5 (Study IV)] The prospective reader study is the only clinical evaluation, but it involves only eight patients. The average scores and 'best image count' are reported without inter-reader agreement statistics, and it is not clear whether the counts in Table 5 are summed over the two readers or represent consensus. Given that the average score advantage of DISCUS over L+S is small (4.63 vs 4.5) and the authors attribute the narrowed separation to MoCo, the evidence for a clinical advantage would be strengthened by per-reader scores, agreement measures (e.g., Cohen's kappa), and a clearer description of the scoring procedure.
  4. [Section 2.8] The free parameters (λ, learning rate, iterations, and the dynamic-code channel count k) are tuned on an additional fully sampled retrospective dataset, but no sensitivity analysis is reported. Since λ directly controls the sparsity of the dynamic codes and thus the claimed manifold dimension, the manuscript should report the tuned values, the range over which performance is stable, and whether the same values are used for the prospective Study IV data. Without this, it is hard to assess whether the reported advantages are robust to parameter choice.
minor comments (5)
  1. [Section 3.2] The text says DISCUS is tested at 'four different acceleration rates, i.e., R = 2, 3, 4, and 5,' but Table 2 also reports R = 6; the sentence and table should be made consistent.
  2. [Section 2.4 / Table 3] In the ablation study, the description says R = 4, but Table 3 does not explicitly repeat the acceleration rate in the caption; please state it clearly to avoid ambiguity.
  3. [Section 2.5] The phrase 'acceleration rate of R = 1 was enabled by lower spatial resolutions and longer temporal footprints' is confusing because R = 1 usually denotes no undersampling; please rephrase to clarify that this is a fully sampled reference acquisition with reduced resolution.
  4. [Throughout] There are several typographical errors, including 'dimensionailty', 'NSME', 'Undersampling' in Section 2.5, and 'not pre-defined' in Section 2.2; a copyedit pass would improve readability.
  5. [Section 2.2] The notation z_t[n] is used for the nth element of the dynamic code, but the paper does not define how the spatial index n is mapped to the 2D code grid; please specify the reshaping explicitly.

Circularity Check

2 steps flagged · score 6.0 of 10

Manifold-dimension 'discovery' reduces to the group-sparsity penalty's own effect; reconstruction benchmarks remain independent.

  1. self definitional [Section 2.2 (Eq. (3), Fig. 1(b)); Section 3.1]
    "Group sparsity ensures that the dynamic code vectors are not only sparse but also share a common support across all time frames, aiding in manifold discovery. [...] After training, the number of non-zero entries in each bzt determines the dimensionality of the underlying manifold, while the values of these non-zero entries capture temporal variations over time."

    Dimensionality is operationally defined as the support size of the dynamic code bzt, and Eq. (3) explicitly penalizes that support with the term λ∥z(1:T)∥2,1, whose entire purpose is to drive rows of zt to zero. Thus the 'discovered' manifold dimension is partly manufactured by the regularizer itself: a small support count is a direct effect of choosing λ>0, not an independent measurement of the image series. Study I checks against known ground truth, but it measures the same variable the penalty is designed to shrink, and the paper reports only 8/10 success for the 2D case, with the two active entries failing to disentangle rotation from translation.

  2. fitted input called prediction [Section 2.8 and Section 3.1]
    "The free parameters across all methods, including λ, learning rate, and number of iterations, were optimized based on NMSE using an additional fully sampled dataset from the retrospective study."

    The sparsity level that controls how many nonzero entries survive in bzt is set by λ, and λ is tuned on data rather than derived from the manifold itself. Reporting the resulting support count as the 'discovered' manifold dimensionality therefore presents a regularizer-strength choice as an empirical finding. The circularity is reinforced by the absence of any reported threshold for what counts as 'nonzero' in Sections 2.3 and 3.1: Adam solutions rarely produce exact zeros, so the count depends on implementation choices as well as on the tuned penalty strength, not on an intrinsic property of the image series.

full rationale

The central circularity is confined to the paper's manifold-discovery narrative. Equation (3) adds a group-sparsity penalty to the dynamic code vectors, and Section 2.2 defines the manifold dimensionality as the number of nonzero entries in those same vectors. Consequently, the claim that DISCUS 'discovers' the manifold dimension is, to a substantial degree, a restatement of the regularizer's effect: the optimizer is explicitly rewarded for producing a small support, and the paper then reads that support off as a property of the data. The Study I validation is helpful but not fully independent, since it checks exactly the variable that the regularization shrinks, and its 8/10 success rate plus the admitted lack of disentanglement show that the count is not a robust invariant. The reconstruction-quality results, by contrast, are not circular in the same way: they compare DISCUS against CS, L+S, DIP, and SG-DIP on simulated and measured LGE data, with code and representative data publicly available, and the hyperparameters, including λ, are tuned on an additional fully sampled dataset. No load-bearing self-citation chain was found; the reference to the authors' ISBI preliminary work [30] is a provenance statement rather than the justification for the method. The overall score reflects the partial circularity of the manifold-dimensionality claim, not an invalidation of the empirical reconstruction comparisons.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

No new physical entities are postulated. The low-dimensional manifold is a modeling construct, not an entity with independent falsifiable handles beyond the image reconstructions. The central claim rests on the hyperparameters listed and the domain assumptions above.

free parameters (4)
  • Lambda (group sparsity strength) = not reported (tuned on validation data)
    Controls trade-off between data consistency and sparsity of dynamic code vectors; effectively sets the typical manifold dimension. Tuned on an additional fully sampled retrospective dataset (Section 2.8).
  • k (number of static code channels) = 3
    Set by hand after observing insensitivity for 2 < k <= 8 (Section 2.2).
  • Training iterations = 10,000
    Tuned early-stopping-like behavior; DISCUS flat between 8,000 and 15,000 iterations while without group sparsity (DGS) overfits past 10,000 (Sections 2.7 and 4).
  • Optimizer schedule (Adam) = LR 0.001, step 500, gamma 0.97
    Standard schedule adopted from DIP practice; no sensitivity analysis reported.
assumptions (6)
  • domain assumption Noise model: circularly symmetric white Gaussian noise b with variance sigma^2 in y = A x + b
    Used throughout to define data consistency (Eq. 1); deviations from white Gaussian noise in real LGE data are not modeled.
  • domain assumption U-Net architecture acts as an implicit natural-image prior (DIP prior)
    Borrowed from Ulyanov et al. [14]; the method's regularization relies on this inductive bias rather than on an explicit prior (Section 2.1).
  • ad hoc to paper Dynamic image series lies on a low-dimensional manifold representable by shared-support dynamic code vectors z_t
    Central modeling assumption of DISCUS: group sparsity on z_(1:T) discovers the support (Eq. 3). It is validated empirically but not proven.
  • domain assumption Coil sensitivity maps from ESPIRiT are accurate enough for the forward operator
    Used to form A_t in Studies III and IV (Section 2.5); sensitivity errors are not propagated in uncertainty estimates.
  • domain assumption Temporal order of frames is uninformative; no smoothness constraint between neighboring frames
    Justified for single-shot LGE where frames are acquired once per heartbeat (Sections 1 and 2.2).
  • ad hoc to paper Hyperparameters tuned on fully sampled retrospective data transfer to prospective undersampled data
    Assumed in Study IV; the paper does not report a separate validation for the prospective protocol.

how reviews work

0 comments
Cite this review

Pith. "Pith review of An unsupervised method for MRI recovery: Deep image prior with structured sparsity." pith.science (2026). https://pith.science/paper/WVX6T32Q

@misc{pith2026250101482,
  author       = {Pith},
  title        = {Pith review of: An unsupervised method for MRI recovery: Deep image prior with structured sparsity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WVX6T32Q}},
  note         = {Machine review of arXiv:2501.01482}
}
read the original abstract

Objective: To propose and validate an unsupervised MRI reconstruction method that does not require fully sampled k-space data. Materials and Methods: The proposed method, deep image prior with structured sparsity (DISCUS), extends the deep image prior (DIP) by introducing group sparsity to frame-specific code vectors, enabling the discovery of a low-dimensional manifold for capturing temporal variations. \discus was validated using four studies: (I) simulation of a dynamic Shepp-Logan phantom to demonstrate its manifold discovery capabilities, (II) comparison with compressed sensing and DIP-based methods using simulated single-shot late gadolinium enhancement (LGE) image series from six distinct digital cardiac phantoms in terms of normalized mean square error (NMSE) and structural similarity index measure (SSIM), (III) evaluation on retrospectively undersampled single-shot LGE data from eight patients, and (IV) evaluation on prospectively undersampled single-shot LGE data from eight patients, assessed via blind scoring from two expert readers. Results: DISCUS outperformed competing methods, demonstrating superior reconstruction quality in terms of NMSE and SSIM (Studies I--III) and expert reader scoring (Study IV). Discussion: An unsupervised image reconstruction method is presented and validated on simulated and measured data. These developments can benefit applications where acquiring fully sampled data is challenging.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

41 extracted references · 39 canonical work pages

  1. [1]

    Low-rank and adaptive sparse signal (LASSI) models for highly accelerated dynamic imaging

    Ravishankar S, Moore BE, Nadakuditi RR, Fessler JA. Low-rank and adaptive sparse signal (LASSI) models for highly accelerated dynamic imaging. IEEE Transactions on Medical Imaging. 2017;36(5):1116–1128

    work page 2017

  2. [2]

    SENSE: sensitivity encoding for fast MRI

    Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE: sensitivity encoding for fast MRI. Magnetic Resonance in Medicine. 1999;42(5):952–962

    work page 1999

  3. [3]

    General- ized autocalibrating partially parallel acqui- sitions (GRAPPA)

    Griswold MA, Jakob PM, Heidemann RM, Nittka M, Jellus V, Wang J, et al. General- ized autocalibrating partially parallel acqui- sitions (GRAPPA). Magnetic Resonance in Medicine. 2002;47(6):1202–1210

    work page 2002

  4. [4]

    ESPIRiT—an eigenvalue approach to autocalibrating parallel MRI: where SENSE meets GRAPPA

    Uecker M, Lai P, Murphy MJ, Virtue P, Elad M, Pauly JM, et al. ESPIRiT—an eigenvalue approach to autocalibrating parallel MRI: where SENSE meets GRAPPA. Magnetic resonance in medicine. 2014;71(3):990–1001

    work page 2014

  5. [5]

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

    Lustig M, Donoho D, Pauly JM. Sparse MRI: The application of compressed sensing for rapid MR imaging. Magnetic Resonance in Medicine. 2007;58(6):1182–1195

    work page 2007

  6. [6]

    Low-rank plus sparse matrix decomposition for acceler- ated dynamic MRI with separation of back- ground and dynamic components

    Otazo R, Candes E, Sodickson DK. Low-rank plus sparse matrix decomposition for acceler- ated dynamic MRI with separation of back- ground and dynamic components. Magnetic resonance in medicine. 2015;73(3):1125–1136

    work page 2015

  7. [7]

    fastMRI: An open dataset and benchmarks for accelerated MRI

    Zbontar J, Knoll F, Sriram A, Muckley MJ, Bruno M, Defazio A, et al. fastMRI: An open dataset and benchmarks for accelerated MRI. arXiv:181108839. 2018

    work page 2018

  8. [8]

    Deep learning for undersampled MRI recon- struction

    Hyun CM, Kim HP, Lee SM, Lee S, Seo JK. Deep learning for undersampled MRI recon- struction. Physics in Medicine & Biology. 2018;63(13):135007

    work page 2018

Show all 41 references
  1. [9]

    OCMR (v1.0)–open- access multi-coil k-space dataset for cardio- vascular magnetic resonance imaging

    Chen C, Liu Y, Schniter P, Tong M, Zareba K, Simonetti O, et al. OCMR (v1.0)–open- access multi-coil k-space dataset for cardio- vascular magnetic resonance imaging. arXiv preprint arXiv:200803410. 2020

    2020

  2. [10]

    Learn- ing a variational network for reconstruction of accelerated MRI data

    Hammernik K, Klatzer T, Kobler E, Recht MP, Sodickson DK, Pock T, et al. Learn- ing a variational network for reconstruction of accelerated MRI data. Magnetic resonance in medicine. 2018;79(6):3055–3071

    2018

  3. [11]

    MoDL: Model-based deep learning architecture for inverse problems

    Aggarwal H, Mani M, Jacob M. MoDL: Model-based deep learning architecture for inverse problems. IEEE Transactions on Medical Imaging. 2018;38(2):394–405. https: //doi.org/10.1109/TMI.2018.2865356

    2018

  4. [12]

    Plug-and-play priors for model based reconstruction

    Venkatakrishnan SV, Bouman CA, Wohlberg B. Plug-and-play priors for model based reconstruction. In: 2013 IEEE global con- ference on signal and information processing. IEEE; 2013. p. 945–948

    2013

  5. [13]

    Plug-and- play methods for magnetic resonance imag- ing: Using denoisers for image recovery

    Ahmad R, Bouman CA, Buzzard GT, Chan S, Liu S, Reehorst ET, et al. Plug-and- play methods for magnetic resonance imag- ing: Using denoisers for image recovery. IEEE Signal Processing Magazine. 2020;37(1):105– 116

    2020

  6. [14]

    Deep image prior

    Ulyanov D, Vedaldi A, Lempitsky V. Deep image prior. In: Proceedings of the IEEE conference on computer vision and pattern recognition; 2018. p. 9446–9454

    2018

  7. [15]

    Deep decoder: Con- cise image representations from untrained non-convolutional networks

    Heckel R, Hand P. Deep decoder: Con- cise image representations from untrained non-convolutional networks. arXiv preprint arXiv:181003982. 2018

    2018

  8. [16]

    The spectral bias of the deep image prior

    Chakrabarty P, Maji S. The spectral bias of the deep image prior. arXiv preprint arXiv:191208905. 2019

    2019

  9. [17]

    Early stopping for deep image prior

    Wang H, Li T, Zhuang Z, Chen T, Liang H, Sun J. Early stopping for deep image prior. arXiv preprint arXiv:211206074. 2021

    2021

  10. [18]

    Robust Self-Guided Deep Image Prior

    Bell E, Liang S, Qu Q, Ravishankar S. Robust Self-Guided Deep Image Prior. In: 2023 IEEE International Conference on Acoustics, Speech and Signal Processing; 2023. p. 1–5

    2023

  11. [19]

    Physics- driven deep learning for computational mag- netic resonance imaging: Combining physics 15 and machine learning for improved medical imaging

    Hammernik K, K¨ ustner T, Yaman B, Huang Z, Rueckert D, Knoll F, et al. Physics- driven deep learning for computational mag- netic resonance imaging: Combining physics 15 and machine learning for improved medical imaging. IEEE signal processing magazine. 2023;40(1):98–114

    2023

  12. [20]

    Deep learning for accelerated and robust MRI reconstruction

    Heckel R, Jacob M, Chaudhari A, Perlman O, Shimron E. Deep learning for accelerated and robust MRI reconstruction. Magnetic Resonance Materials in Physics, Biology and Medicine. 2024;37(3):335–368

    2024

  13. [21]

    Time-dependent deep image prior for dynamic MRI

    Yoo J, Jin KH, Gupta H, Yerly J, Stuber M, Unser M. Time-dependent deep image prior for dynamic MRI. IEEE Transactions on Medical Imaging. 2021;40(12):3337–3348

    2021

  14. [22]

    Dynamic imaging using a deep generative SToRM (Gen-SToRM) model

    Zou Q, Ahmed AH, Nagpal P, Kruger S, Jacob M. Dynamic imaging using a deep generative SToRM (Gen-SToRM) model. IEEE Transactions on Medical Imag- ing. 2021;40(11):3102–3112

    2021

  15. [23]

    Dynamic imaging using deep bi-linear unsupervised representation (DEBLUR)

    Ahmed AH, Zou Q, Nagpal P, Jacob M. Dynamic imaging using deep bi-linear unsupervised representation (DEBLUR). IEEE transactions on medical imaging. 2022;41(10):2693–2703

    2022

  16. [24]

    A low-rank deep image prior reconstruction for free- breathing ungated spiral functional CMR at 0.55 T and 1.5 T

    Hamilton JI, Truesdell W, Galizia M, Bur- ris N, Agarwal P, Seiberlich N. A low-rank deep image prior reconstruction for free- breathing ungated spiral functional CMR at 0.55 T and 1.5 T. Magnetic Resonance Materials in Physics, Biology and Medicine. 2023;36(3):451–464

    2023

  17. [25]

    Dynamic imaging using motion-compensated smoothness regulariza- tion on manifolds (MoCo-SToRM)

    Zou Q, Torres LA, Fain SB, Higano NS, Bates AJ, Jacob M. Dynamic imaging using motion-compensated smoothness regulariza- tion on manifolds (MoCo-SToRM). Physics in Medicine & Biology. 2022;67(14):144001

    2022

  18. [26]

    Implementation and validation of a three- dimensional cardiac motion estimation net- work

    Morales MA, Izquierdo-Garcia D, Aganj I, Kalpathy-Cramer J, Rosen BR, Catana C. Implementation and validation of a three- dimensional cardiac motion estimation net- work. Radiology: Artificial Intelligence. 2019;1(4):e180080

    2019

  19. [27]

    A bidirectional registration neural network for cardiac motion tracking using cine MRI images

    Lu J, Jin R, Wang M, Song E, Ma G. A bidirectional registration neural network for cardiac motion tracking using cine MRI images. Computers in Biology and Medicine. 2023;160:107001

    2023

  20. [28]

    End- to-end deep learning of non-rigid groupwise registration and reconstruction of dynamic MRI

    Yang J, K¨ ustner T, Hu P, Li` o P, Qi H. End- to-end deep learning of non-rigid groupwise registration and reconstruction of dynamic MRI. Frontiers in cardiovascular medicine. 2022;9:880186

    2022

  21. [29]

    Attention-aware non-rigid image registration for accelerated MR imaging

    Ghoul A, Pan J, Lingg A, K¨ ubler J, Krumm P, Hammernik K, et al. Attention-aware non-rigid image registration for accelerated MR imaging. IEEE transactions on medical imaging. 2024;43(8):3013–3026

    2024

  22. [30]

    Deep Image prior with StruCtUred Sparsity (DISCUS) for dynamic MRI reconstruction

    Sultan MA, Chen C, Liu Y, Lei X, Ahmad R. Deep Image prior with StruCtUred Sparsity (DISCUS) for dynamic MRI reconstruction. In: 2024 IEEE International Symposium on Biomedical Imaging (ISBI). IEEE; 2024. p. 1–5

    2024

  23. [31]

    Model selection and esti- mation in regression with grouped variables

    Yuan M, Lin Y. Model selection and esti- mation in regression with grouped variables. Journal of the Royal Statistical Society Series B: Statistical Methodology. 2006;68(1):49–67

    2006

  24. [32]

    Free-breathing, motion-corrected late gadolinium enhance- ment is robust and extends risk stratification to vulnerable patients

    Piehler KM, Wong TC, Puntil KS, Zareba KM, Lin K, Harris DM, et al. Free-breathing, motion-corrected late gadolinium enhance- ment is robust and extends risk stratification to vulnerable patients. Circulation: Cardio- vascular Imaging. 2013;6(3):423–432

    2013

  25. [33]

    Dynamic MRI using smoothness regularization on manifolds (SToRM)

    Poddar S, Jacob M. Dynamic MRI using smoothness regularization on manifolds (SToRM). IEEE Transactions on Medical Imaging. 2015;35(4):1106–1115

    2015

  26. [34]

    MRXCAT: Realistic numerical phantoms for cardiovascular magnetic resonance

    Wissmann L, Santelli C, Segars WP, Kozerke S. MRXCAT: Realistic numerical phantoms for cardiovascular magnetic resonance. Jour- nal of Cardiovascular Magnetic Resonance. 2014;16(1):1–11

    2014

  27. [35]

    Analytical model for the approx- imation of hysteresis loop and its application to the scanning tunneling microscope

    Lapshin R V. Analytical model for the approx- imation of hysteresis loop and its application to the scanning tunneling microscope. Review of Scientific Instruments. 1995;66(9):4718– 4730

    1995

  28. [36]

    Technical Report (v1.0)–Pseudo-random 16 Cartesian Sampling for Dynamic MRI

    Joshi M, Pruitt A, Chen C, Liu Y, Ahmad R. Technical Report (v1.0)–Pseudo-random 16 Cartesian Sampling for Dynamic MRI. arXiv preprint arXiv:220603630. 2022;https://doi. org/10.48550/arXiv.2206.03630

    2022 doi arXiv

  29. [37]

    Phase-sensitive inversion recov- ery for detecting myocardial infarction using gadolinium-delayed hyperenhance- ment

    Kellman P, Arai AE, McVeigh ER, Aletras AH. Phase-sensitive inversion recov- ery for detecting myocardial infarction using gadolinium-delayed hyperenhance- ment. Magnetic Resonance in Medicine. 2002;47(2):372–383

    2002

  30. [38]

    Array compression for MRI with large coil arrays

    Buehrer M, Pruessmann KP, Boesiger P, Kozerke S. Array compression for MRI with large coil arrays. Magnetic Resonance in Medicine. 2007;57(6):1131–1139

    2007

  31. [39]

    Surface Coil Intensity Correction for MRI

    Lei X, Schniter P, Chen C, Sultan MA, Ahmad R. Surface Coil Intensity Correction for MRI. In: 2024 IEEE International Sym- posium on Biomedical Imaging (ISBI); 2024. p. 1–5

    2024

  32. [40]

    Motion cor- rection for myocardial T1 mapping using image registration with synthetic image esti- mation

    Xue H, Shah S, Greiser A, Guetter C, Littmann A, Jolly MP, et al. Motion cor- rection for myocardial T1 mapping using image registration with synthetic image esti- mation. Magnetic resonance in medicine. 2012;67(6):1644–1655

    2012

  33. [41]

    Image quality assessment: from error visibility to structural similarity

    Wang Z, Bovik AC, Sheikh HR, Simoncelli EP. Image quality assessment: from error visibility to structural similarity. IEEE trans- actions on image processing. 2004;13(4):600– 612. 17

    2004

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.