ACE-Net: AutofoCus-Enhanced Convolutional Network for Field Imperfection Estimation with application to high b-value spiral Diffusion MRI

Daniel Abraham; Kawin Setsompop; Mengze Gao; Nan Wang; Xiaozhi Cao; Zachary Shah

REVIEW 4 major objections 5 minor 7 references

ACE-Net: AutofoCus-Enhanced Convolutional Network for Field Imperfection Estimation with application to high b-value spiral Diffusion MRI

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A convolutional network, ACE-Net, estimates the spatiotemporal B0 and eddy-current fields that corrupt spiral diffusion MRI directly from the blurred images themselves, using autofocus metrics and a compact basis, and reconstructs…

desk verdict Promising integration of autofocus + CNN for field estimation, but the 'accurate' claim rests on unquantified visuals and an unvalidated basis order; needs a residual analysis against existing Skope data. read the letter →

arxiv 2411.14630 v1 pith:PMUJ3CMZ submitted 2024-11-21 physics.med-ph cs.LGeess.IV

Mengze Gao , Zachary Shah , Xiaozhi Cao , Nan Wang , Daniel Abraham , Kawin Setsompop This is my paper · ORCID

classification physics.med-phcs.LGeess.IV

keywords spiraldiffusionMRIfieldimperfectionestimationautofocusmetriceddycurrentsB0inhomogeneitydeeplearningunrollednetworksphericalharmonics

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 seeks to establish that a deep convolutional network can recover the magnetic-field imperfections that blur and distort high-b-value spiral diffusion MRI, directly from the images being corrected. The method, ACE-Net, feeds autofocus blur metrics and slice information into a network that outputs coefficients of a compact physical basis for the field: spatial spherical harmonics up to third order multiplied by temporal polynomials up to third order. The payoff is that scans no longer need lengthy calibration acquisitions or external field-probe measurements, which are time-consuming and can be invalidated by scanner heating or subject motion. On two volunteer scans at b=3000, the estimated fields closely matched ground-truth measurements, and the corrected DTI showed white-matter tracts that were not discernible before correction.

What carries the argument

The load-bearing mechanism is the autofocus blur metric combined with a compact basis representation. The autofocus metric measures how blurred an image is at a given off-resonance frequency offset; minimizing it locates the field error, but the metric is noisy and prone to local minima, so the network supplies a learned prior and the basis constrains the solution. The compact basis, $\phi(\mathbf{r},t) = \sum_n \phi_n(\mathbf{r})\delta_n(t)$, with third-order spatial spherical harmonics and third-order temporal polynomials, reduces the unknown field to a small set of coefficients, making the estimation tractable. The unrolled architecture adds a data-consistency step that re-encodes the estimated field into the forward model and updates the blurred images and autofocus metrics, counteracting hallucination.

What would settle it

Acquire a spiral diffusion scan at b=3000 while deliberately inducing an eddy field with a fourth-order spherical-harmonic spatial component or a temporal variation faster than a third-order polynomial, measure the true field with a field-probe system, and run ACE-Net; if the estimated field misses the injected component and residual blur remains after correction, the compact-basis assumption is falsified.

Watch

Extended reading notes

Core claim

The paper's central claim is that ACE-Net can estimate spatiotemporal field imperfections from the corrupted spiral diffusion data alone, with no external calibration. Static B0 inhomogeneity is estimated first from the b=0 image, using autofocus metrics across a ±120 Hz range, narrowed to ±40 Hz by a rough CNN B0 estimate, to produce a refined B0 map. Spatiotemporal eddy-current and dynamic B0 fields are then estimated per diffusion direction as $\phi(\mathbf{r},t) = \sum_n \phi_n(\mathbf{r})\delta_n(t)$, with $\phi_n$ spatial spherical harmonics and $\delta_n$ temporal polynomials truncated at third order based on field-probe data. The network outputs the basis coefficients, and an unrolled version with a data-consistency block re-encodes the estimated field into the forward model to prevent hallucination. In the demonstrated application, the estimated fields matched the ground-truth field-probe and multi-echo GRE measurements, and incorporating them into reconstruction removed blur and made the white-matter tracts clearly visible.

Load-bearing premise

The method assumes that every field error it needs to fix can be written as a few smooth spatial patterns (spherical harmonics up to third order) changing along a few smooth time curves (polynomials up to third order); if a real scan contains sharper or faster variations, the network cannot represent them, so the correction would fail no matter how well the network was trained.

Editorial extensions

If this is right

High-b-value spiral diffusion protocols can drop dedicated calibration scans and field-probe measurements for B0 and eddy correction, since ACE-Net estimates the fields from the data already acquired.
Corrected reconstructions make white-matter fiber tracts visible in 22-direction DTI, so quantitative diffusion metrics in affected regions should become more reliable.
The unrolled data-consistency variant provides a check against network hallucination by requiring the estimated field to reproduce the measured k-space data.
Because the field is represented by a small coefficient set over physical bases, the method also produces a compact characterization of the scanner's eddy-current state during a scan.
The same autofocus-plus-network estimation principle is intended by the authors to extend to EPI and motion-robust reconstruction, where the same class of spatiotemporal field errors degrades image quality.

Reading between the lines

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

Editorial inference: the third-order spatial/temporal basis is the most fragile component; fields with sharp structure near metal or the sinuses, or fast transient eddy behavior, would fall outside what the network can represent, so a learned or adaptive basis is the natural next step.
Editorial inference: because the autofocus metric is a generic sharpness signal, the same architecture could be applied to other phase-error sources that lack external references, such as motion-induced phase or chemical shift, provided a physical basis for those errors is available.
Editorial inference: a cross-platform generalization test would reveal whether ACE-Net learned scanner-specific eddy dynamics or a universal physical constraint; if estimates degrade on another scanner, the training distribution would need to cover more hardware.
Editorial inference: with only two volunteer test scans, a larger cohort study is needed to confirm that the estimates stay accurate when B0 drifts during long protocols and when subject motion changes the field during the acquisition.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

You asked about ACE-Net. Quick take: this is a plausible integration of known pieces, but the abstract-level evidence doesn't support the "accurate estimation" claim as stated.

What's genuinely new: combining autofocus metrics with a physics-informed CNN and a compact spatiotemporal basis, plus the unrolled refinement for robustness. Each ingredient exists in the literature (Noll, Anderson, ResoNet, SAFE, Valsamis), but the combination for high-b spiral diffusion without external calibration is a reasonable workflow improvement. The authors also deserve credit for acquiring Skope and multi-echo GRE ground truth on the two test subjects and for training on separate data—so the evaluation is not circular in the naive sense.

The soft spots are real and load-bearing. First, no quantitative field-error metric anywhere. The figures show visual similarity, but you cannot rule out that the network finds a field that improves sharpness while being systematically wrong in ways that matter for DTI. Second, the spatiotemporal basis order (3rd-order spherical harmonics × 3rd-order polynomials) is justified from field-probe data at lower b-values, and the paper never reports a residual analysis against the b=3000 Skope ground truth it already has. If real eddy fields at b=3000 contain higher spatial modes or temporal components beyond cubic, the network's output space cannot contain the true field, and every downstream correction is biased. This is the weakest joint, and the stress-test note is right to flag it. Third, two test volunteers is thin for a claim of "accurate" estimation; that is a feasibility demonstration, not validation. Fourth, the training data come from different protocols and scanner sessions (b1000/2000 with different TEs, synthesized DWIs from BUDA-EPI), which is fine for an abstract but leaves cross-b-value generalization unexamined.

I want to be fair: this is an extended abstract, so we shouldn't expect full reproducibility or error bars. But the authors' own conclusion goes beyond what they show. The one missing experiment that would transform this is a quantitative residual of estimated vs. Skope field at b=3000 (RMS or percentile Hz, plus a blur metric before/after). They have the ground truth; they just didn't report the numbers.

Recommendation: I would not send this to referees as-is. It reads as a work-in-progress abstract, and the evidence is too thin for a serious journal. But the method has merit, and if the authors add the residual analysis, more subjects, and code/data, it becomes a refereed paper. For now: desk reject with a clear signal to strengthen and resubmit.

Referee Report

4 major / 5 minor

Summary. The paper proposes ACE-Net, a deep-learning method for estimating spatiotemporal field imperfections (B0 inhomogeneity and diffusion-encoding-induced eddy currents) in high-b-value spiral diffusion MRI. The method combines autofocus blur metrics with a CNN and uses a compact basis of 3rd-order spherical harmonics in space and 3rd-order polynomials in time to represent the field. A static B0 map is estimated from a b=0 image, and a subsequent network estimates per-diffusion-direction spatiotemporal eddy/dB0 fields, with an optional unrolled data-consistency refinement. Training data are synthesized from previously acquired B0 maps, MRF data, BUDA-EPI DWIs, and Skope measurements at b=1000/2000, while testing is performed on two volunteers scanned with b=3000 spiral diffusion with multi-echo GRE and Skope measurements as ground truth. The results are presented qualitatively through figures showing estimated fields and corrected images.

Significance. If the claimed accuracy were quantitatively established, ACE-Net would be a practically valuable contribution: it could eliminate scan-time calibration for eddy-current and B0 correction in high-b-value spiral diffusion MRI, a setting where external field probes and lengthy calibration scans are burdensome. The paper has some notable strengths: the evaluation uses external ground truth (multi-echo GRE and Skope), the training and test data are separate, and the unrolled variant is a sensible attempt to reduce hallucination risk. However, the evidence as presented is not sufficient to support the abstract's 'accurate estimation' claim, and the central modeling assumption about the basis order is not validated on the target b=3000 protocol. The work is therefore best viewed as a promising proof-of-concept that requires stronger quantitative validation before its main claims can be accepted.

major comments (4)

[Results, Figs. 3-5] The evaluation is entirely qualitative. No quantitative field-error metric (e.g., RMS or percentile error in Hz against the Skope ground truth), no image-quality metric (e.g., sharpness, SSIM, or blur reduction), and no error bars or per-volunteer breakdown are reported. With only two test volunteers, visual inspection of selected slices is insufficient to support the abstract's claim of 'accurate estimation' and 'high quality image reconstruction'. The authors should report quantitative residuals between estimated and ground-truth fields (at least on the two test volunteers, ideally across slices and diffusion directions) and quantitative measures of image-quality improvement.
[Methods, 'Spatiotemporal eddy and dB0 fields'] The compact basis representation (3rd-order spatial spherical harmonics times 3rd-order temporal polynomials) is justified only by 'field-probe data' without specifying which protocols or b-values those data came from. Because this basis defines the output space of the network, any field component outside this subspace at b=3000 cannot be represented, causing a systematic bias regardless of training quality. The authors should provide a basis-truncation analysis on the b=3000 Skope ground truth (e.g., residual field energy or Hz error as a function of expansion order) to demonstrate that the chosen order is adequate for the target protocol.
[Methods, 'Data'] The spatiotemporal training data are derived from Skope measurements at b=1000 and b=2000 with different mixing times and TEs than the b=3000 test protocol, supplemented by synthesized non-principal diffusion directions. No evidence is given that eddy-current fields at b=3000 lie in the same distribution after the 30% coefficient augmentation. The cross-b-value generalization is a load-bearing assumption and should be explicitly tested, for example by comparing the network's b=3000 field estimates against the Skope ground truth with quantitative metrics, as requested above.
[Results, Fig. 4] The text states that the unrolled ACE-Net 'outperformed the CNN' in field-parameter estimation, but no numerical results or statistical comparison are provided. If the unrolled variant is claimed to be superior, the authors should report quantitative error metrics for both variants, ideally across multiple test cases, to substantiate this comparison.

minor comments (5)

[Methods, 'Static B0 inhomogeneity'] The autofocus metric definition contains typographical artifacts in the equation (e.g., misplaced parentheses and superscript notation); please rewrite it clearly with standard LaTeX.
[Methods, 'Static B0 inhomogeneity'] The choice of autofocus search range (±120 Hz at 10 Hz increments) and the reduction to a valid 40 Hz range are described but not justified; a brief explanation of how these parameters affect performance would help.
[Methods, 'Data'] The training data synthesis is described only briefly; please specify the forward-model details (e.g., how spiral k-space data are generated from the B0 maps and synthesized T2-w images) and the exact augmentation procedure for the basis coefficients.
[General] The figures are referenced as 'Fig.3' and 'Fig.4' inconsistently in the Results section; please renumber and reference all figures consistently and ensure each figure is called out in order.
[General] No information is provided about network training details (loss functions, optimizer, learning rate, number of epochs, or computational cost); adding a short training-details section would aid reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the claimed estimates are checked against external ground truth and trained on non-overlapping data; the basis-order choice is an explicit modeling assumption, not a disguised input.

full rationale

I traced the derivation chain for both B0 and spatiotemporal field estimation. The B0 ACE-Net is trained on B0 maps and synthetic spiral data derived from previously acquired 3D-MRF datasets, and tested on separate volunteers with multi-echo GRE B0 maps as ground truth. The spatiotemporal ACE-Net is trained on Skope measurements at b=1000/2000 with augmentations, and tested on b=3000 spiral data with Skope as ground truth. The test data are not used for training or fitting, so the 'accurate estimation' claim is not derived from the test values by construction. The compact representation as 3rd-order spherical harmonics times 3rd-order temporal polynomials is presented as an empirical modeling choice based on field-probe data, not as a prediction derived from the network; any failure of that representation would be a correctness limitation, not circularity. The only self-citation (SAFE, ref. 6) provides an initial rough B0 estimate used to focus the autofocus metric search range; this is a component of the pipeline, but the network's final output is evaluated against external ground truth, so the self-citation is not load-bearing for the central claim. No equation reduces to its own input, no fitted parameter is renamed as a prediction, and no uniqueness theorem from the authors' prior work is invoked. The paper's own statement that 'future work will include rigorous validation across protocols and scanner platforms' acknowledges residual generalization risk, which is a scientific caveat rather than a circular step. Overall, the derivation is self-contained with respect to the evaluation performed.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The method relies on a compact basis representation of field imperfections, on synthetic training data assumed to be faithful, and on autofocus metrics as meaningful blur indicators. These are reasonable modeling choices but are not independently verified beyond qualitative results on two subjects.

free parameters (5)

Spatial spherical-harmonic order = 3
Empirically chosen from field-probe data to represent eddy/dB0 fields; truncation limits the representable field shapes (Methods, spatiotemporal eddy and dB0 fields).
Temporal polynomial order = 3
Same empirical choice as the spatial order; limits the temporal variation of the estimated fields.
Autofocus search range and increment = +/-120 Hz at 10 Hz steps, valid range 40 Hz
Hand-selected to balance local minima and computation, based on a truncated 12.5 ms spiral acquisition.
Augmentation variation for basis coefficients = 30%
Used to synthesize training data for non-principal diffusion directions; chosen by hand to create diversity.
CNN initial B0 search constraint = within 40 Hz of B0-rough
The refined B0 search is restricted to a 40 Hz window around a rough CNN estimate to avoid autofocus local minima.

assumptions (5)

domain assumption The eddy/dB0 field can be represented by 3rd-order spatial spherical harmonics and 3rd-order temporal polynomials.
Stated in Methods as an empirical determination from field-probe data. The completeness of this basis is assumed and not proven for b=3000.
domain assumption The autofocus blurring metric (imaginary part after background phase removal) is a valid indicator of off-resonance error.
Adopted from Noll et al. and Anderson et al.; the network uses these metrics as inputs without demonstrating their reliability in all test regions.
domain assumption Synthesized training data generated from 3D-MRF, PD/T2 maps, and Skope measurements faithfully represent real spiral diffusion data at b=3000.
The forward-model-based synthesis is described in Data, but no comparison of synthetic versus real image statistics is provided.
domain assumption Eddy-current measurements at b=1000/2000, with 30% coefficient variation and a linear model for non-principal directions, transfer to the b=3000 test protocol.
Training data are at lower b-values than the test data; the linear eddy-current model for synthesis is a strong assumption.
domain assumption The CNN-based rough B0 estimate (SAFE) is accurate enough to constrain the autofocus search to a 40 Hz window.
The method relies on this prior estimate to avoid local minima, but its failure modes are not characterized.

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Cite this review

Pith. "Pith review of ACE-Net: AutofoCus-Enhanced Convolutional Network for Field Imperfection Estimation with application to high b-value spiral Diffusion MRI." pith.science (2026). https://pith.science/paper/PMUJ3CMZ

@misc{pith2026241114630,
  author       = {Pith},
  title        = {Pith review of: ACE-Net: AutofoCus-Enhanced Convolutional Network for Field Imperfection Estimation with application to high b-value spiral Diffusion MRI},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PMUJ3CMZ}},
  note         = {Machine review of arXiv:2411.14630}
}

read the original abstract

Spatiotemporal magnetic field variations from B0-inhomogeneity and diffusion-encoding-induced eddy-currents can be detrimental to rapid image-encoding schemes such as spiral, EPI and 3D-cones, resulting in undesirable image artifacts. In this work, a data driven approach for automatic estimation of these field imperfections is developed by combining autofocus metrics with deep learning, and by leveraging a compact basis representation of the expected field imperfections. The method was applied to single-shot spiral diffusion MRI at high b-values where accurate estimation of B0 and eddy were obtained, resulting in high quality image reconstruction without need for additional external calibrations.

Figures

Figures reproduced from arXiv: 2411.14630 by the authors.

**Figure 1.** Network architecture for B0 field estimation. The inputs to the network are diffusionweighted images (DWI) corrupted by B0 and eddy current fields, slice location, and autofocus metrics at multiple frequency offsets. The output is the estimated B0 map. A frequency selection mask based on an initial rough B0 estimation is used to select autofocus metrics within the appropriate frequency range. The network comprises … view at source ↗

**Figure 2.** Network architecture for spatiotemporal eddy current and dB0 field estimation. (a) The Spatiotemporal ACE-Net structure: the inputs are B0-corrected DWIs, slice location, and autofocus metrics at the center frequency. The outputs are the spatiotemporal field parameters, which are further used to characterize eddy current and dB0 fields. (b) The unrolled Spatiotemporal ACE-Net structure: the blurred DWIs and autofocu… view at source ↗

**Figure 3.** (a) B0 field estimation results. The rough B0 estimation shows high similarity to the ground truth. By utilizing autofocus metrics at different frequencies, the fine B0 estimation further improves accuracy, ultimately achieving results with high correspondence to the ground truth. The ground truth B0 map was acquired via multi-echo EPI. (b) After B0 field correction, B0 blur artifacts in certain areas are mitigated … view at source ↗

Figures from the paper (1 more)

**Figure 5.** Figure 5: Diffusion Tensor Images (DTIs) reconstructed using 22-direction DWIs and a b = 0 image. (a) Reconstruction before B0 and eddy current field estimation: the white matter fiber tracts are difficult to discern. (b) Reconstruction after B0 and eddy current field estimation…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

7 extracted references · 7 canonical work pages

[1]

#$) through a range of off-resonance frequencies: 𝐼!

ACE-Net: AutofoCus-Enhanced Convolutional Network for Field Imperfection Estimation with application to high b-value spiral Diffusion MRI Mengze Gao1, Zachary Shah2, Xiaozhi Cao2, Nan Wang2, Daniel Abraham2, Kawin Setsompop1,2 1 Department of Radiology, Stanford University, Stanford, CA, USA 2 Department of Electrical Engineering, Stanford University, Sta...

work page 2000
[2]

Single‐shot spiral imaging enabled by an expanded encoding model: D emonstration in diffusion MRI

Wilm, Bertram J., et al. "Single‐shot spiral imaging enabled by an expanded encoding model: D emonstration in diffusion MRI." Magnetic resonance in medicine 77.1 (2017): 83-91

work page 2017
[3]

Deblurring for non‐2D Fourier transform magnetic resonance imaging

Noll, Douglas C., et al. "Deblurring for non‐2D Fourier transform magnetic resonance imaging." Magnetic Resonance in Medicine 25.2 (1992): 319-333

work page 1992
[4]

ResoNet: Noise-Trained Physics-Informed MRI Off-Resonance Correction

De Goyeneche Macaya, Alfredo, et al. "ResoNet: Noise-Trained Physics-Informed MRI Off-Resonance Correction." Advances in Neural Information Processing Systems 36 (2024)

work page 2024
[5]

Characterization and correction of time‐varying eddy currents for diffusion MRI

Valsamis, Jake J., Paul I. Dubovan, and Corey A. Baron. "Characterization and correction of time‐varying eddy currents for diffusion MRI." Magnetic Resonance in Medicine 87.5 (2022): 2209-2223

work page 2022
[6]

Sequence adaptive field-imperfection estimation (SAFE): retrospective estimation and correction of $B_1^+$ and $B_0$ inhomogeneities for enhanced MRF quantification

Gao, Mengze, et al. "Sequence adaptive field-imperfection estimation (SAFE): retrospective estimation and correction of $ B_1^+ $ and $ B_0 $ inhomogeneities for enhanced MRF quantification." arXiv preprint arXiv:2312.09488 (2023)

work page Pith review arXiv 2023
[7]

Distortion‐free, high‐isotropic‐resolution diffusion MRI with gSlider BUDA‐EPI and multicoil dynamic B0 shimming

Liao, Congyu, et al. "Distortion‐free, high‐isotropic‐resolution diffusion MRI with gSlider BUDA‐EPI and multicoil dynamic B0 shimming." Magnetic resonance in medicine 86.2 (2021): 791-803. Figure

work page 2021

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

#$) through a range of off-resonance frequencies: 𝐼!

ACE-Net: AutofoCus-Enhanced Convolutional Network for Field Imperfection Estimation with application to high b-value spiral Diffusion MRI Mengze Gao1, Zachary Shah2, Xiaozhi Cao2, Nan Wang2, Daniel Abraham2, Kawin Setsompop1,2 1 Department of Radiology, Stanford University, Stanford, CA, USA 2 Department of Electrical Engineering, Stanford University, Sta...

work page 2000

[2] [2]

Single‐shot spiral imaging enabled by an expanded encoding model: D emonstration in diffusion MRI

Wilm, Bertram J., et al. "Single‐shot spiral imaging enabled by an expanded encoding model: D emonstration in diffusion MRI." Magnetic resonance in medicine 77.1 (2017): 83-91

work page 2017

[3] [3]

Deblurring for non‐2D Fourier transform magnetic resonance imaging

Noll, Douglas C., et al. "Deblurring for non‐2D Fourier transform magnetic resonance imaging." Magnetic Resonance in Medicine 25.2 (1992): 319-333

work page 1992

[4] [4]

ResoNet: Noise-Trained Physics-Informed MRI Off-Resonance Correction

De Goyeneche Macaya, Alfredo, et al. "ResoNet: Noise-Trained Physics-Informed MRI Off-Resonance Correction." Advances in Neural Information Processing Systems 36 (2024)

work page 2024

[5] [5]

Characterization and correction of time‐varying eddy currents for diffusion MRI

Valsamis, Jake J., Paul I. Dubovan, and Corey A. Baron. "Characterization and correction of time‐varying eddy currents for diffusion MRI." Magnetic Resonance in Medicine 87.5 (2022): 2209-2223

work page 2022

[6] [6]

Sequence adaptive field-imperfection estimation (SAFE): retrospective estimation and correction of $B_1^+$ and $B_0$ inhomogeneities for enhanced MRF quantification

Gao, Mengze, et al. "Sequence adaptive field-imperfection estimation (SAFE): retrospective estimation and correction of $ B_1^+ $ and $ B_0 $ inhomogeneities for enhanced MRF quantification." arXiv preprint arXiv:2312.09488 (2023)

work page Pith review arXiv 2023

[7] [7]

Distortion‐free, high‐isotropic‐resolution diffusion MRI with gSlider BUDA‐EPI and multicoil dynamic B0 shimming

Liao, Congyu, et al. "Distortion‐free, high‐isotropic‐resolution diffusion MRI with gSlider BUDA‐EPI and multicoil dynamic B0 shimming." Magnetic resonance in medicine 86.2 (2021): 791-803. Figure

work page 2021