Fast Reconstruction of Motion-Corrupted Data with Mobile-GRAPPA: Motion and dB0 Inhomogeneity Correction Leveraging Efficient GRAPPA

Aizada Nurdinova; Daniel Abraham; Daniel Polak; Kawin Setsompop; Nan Wang; Stephen Cauley; Xiaozhi Cao; Yimeng Lin

arxiv: 2511.06257 · v2 · pith:5DEESD76new · submitted 2025-11-09 · 📡 eess.SP

Fast Reconstruction of Motion-Corrupted Data with Mobile-GRAPPA: Motion and dB0 Inhomogeneity Correction Leveraging Efficient GRAPPA

Yimeng Lin , Nan Wang , Daniel Abraham , Daniel Polak , Xiaozhi Cao , Aizada Nurdinova , Stephen Cauley , Kawin Setsompop This is my paper

Pith reviewed 2026-05-18 00:02 UTC · model grok-4.3

classification 📡 eess.SP

keywords motion correctiondB0 inhomogeneityGRAPPASENSE reconstructionMRIk-space cleaningparallel imaging

0 comments

The pith

Mobile-GRAPPA cleans motion and dB0 corrupted k-space data with position-specific GRAPPA kernels so standard SENSE can reconstruct it quickly and accurately.

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

The paper addresses the fact that detailed motion and magnetic field tracking during MRI scans makes full integration into reconstruction methods like Aligned-SENSE too slow for practical use. It proposes Mobile-GRAPPA as a preprocessing step that removes these corruptions from k-space using local operators. A lightweight multilayer perceptron trains a family of kernels tailored to each k-space position. After this cleaning, conventional SENSE produces the final images. Tests on whole-brain GRE and EPTI data with hundreds of motion trackings confirm the method works with almost no extra time compared to the hours or days required by direct integration.

Core claim

Mobile-GRAPPA is a k-space cleaning approach that uses a family of position-specific GRAPPA kernels, trained efficiently by a lightweight multilayer perceptron, to remove motion and dB0-induced phase corruptions. The cleaned data then supports accurate reconstruction by standard SENSE, delivering high-quality results with only negligible computational cost even when 500 to 1600 motion and field measurements are available during a scan.

What carries the argument

Mobile-GRAPPA kernels: a set of local GRAPPA operators generated position-by-position via MLP to correct motion and dB0 phase errors in k-space before conventional parallel imaging reconstruction.

If this is right

Detailed motion navigation data from 1620 trackings can be used in 10-minute GRE scans without prohibitive reconstruction time.
EPTI scans with 544 trackings over 2 minutes become feasible for standard SENSE after cleaning.
Reconstruction time stays close to that of uncorrected SENSE rather than exceeding 10 hours or 10 days.
The approach works for both gradient-echo and echo-planar time-resolved imaging sequences under strong motion.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Separating correction into a fast k-space cleaning step may let the same kernels combine with reconstruction methods other than SENSE.
The lightweight MLP training opens the possibility of adapting kernels on the fly for different motion patterns within one exam.
This preprocessing style could support motion handling in higher-resolution protocols where full joint reconstruction remains too costly.

Load-bearing premise

That kernels trained by the MLP remove motion and dB0 effects accurately enough that standard SENSE produces images without new artifacts introduced by the cleaning step.

What would settle it

Apply Mobile-GRAPPA cleaning plus SENSE and full Aligned-SENSE to the same highly motion-corrupted GRE dataset and check whether the two final images agree within noise levels while the first method finishes in minutes rather than hours.

read the original abstract

Advanced motion navigations now enable rapid tracking of subject motion and dB0-induced phase, but accurately incorporating this high-temporal-resolution information into SENSE (Aligned-SENSE) is often computationally prohibitive. We propose "Mobile-GRAPPA", a k-space "cleaning" approach that uses local GRAPPA operators to remove motion and dB0 related corruption so that the resulting data can be reconstructed with standard SENSE. We efficiently train a family of k-space-position-specific Mobile-GRAPPA kernels via a lightweight multilayer perceptron (MLP) and apply them across k-space to generate clean data. In experiments on highly motion-corrupted 1-mm whole-brain GRE (Tacq = 10 min; 1,620 motion/dB0 trackings) and EPTI (Tacq = 2 min; 544 trackings), Mobile-GRAPPA enabled accurate reconstruction with negligible time penalty, whereas full Aligned-SENSE was impractical (reconstruction times > 10 h for GRE and > 10 days for EPTI). These results show that Mobile-GRAPPA incorporates detailed motion and dB0 tracking into SENSE with minimal computational overhead, enabling fast, high-quality reconstructions of challenging data.

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.

Desk Editor's Note private letter to a colleague

Mobile-GRAPPA gives a workable speed fix for motion and dB0 tracking inside SENSE by pre-cleaning k-space with MLP-generated local kernels, though the validation details are still thin.

read the letter

The main thing to know is that Mobile-GRAPPA cleans motion and dB0 corrupted k-space using MLP-trained local GRAPPA kernels so that standard SENSE can be used instead of the much slower Aligned-SENSE. This design is new in how it leverages the MLP for position-dependent kernels to handle the corrections efficiently. It builds directly on GRAPPA and SENSE but applies them in a pre-processing step for the tracked data. The idea of training a family of kernels via a lightweight network avoids retraining or heavy computation at each position. The experiments demonstrate clear practical value. On the GRE scan with over 1600 motion trackings and the EPTI with over 500, the method runs fast while the full approach does not. This removes a barrier for protocols that need detailed tracking over long acquisitions. The soft spot is the limited evidence on image quality. The abstract mentions accurate reconstruction but skips quantitative metrics or direct comparisons to a motion-free reference. It is possible that the kernel application introduces new phase inconsistencies or leaves some ghosts, especially if the motion has components not well modeled by local operators. The stress-test point about whether the cleaning produces data equivalent to what Aligned-SENSE would give is a real one here, since no consistency error or artifact quantification is provided. Overall this targets MRI engineers and researchers focused on motion-robust imaging. A reader interested in efficient reconstruction pipelines would find the speed results useful, though they should look for the full figures to assess the output quality. I think it deserves peer review to examine the implementation details and validate the claims with more data. The core engineering is sound enough that referees could help strengthen the validation.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes Mobile-GRAPPA, a k-space cleaning method that trains a family of position-specific GRAPPA kernels via a lightweight MLP to remove motion and dB0-induced phase corruptions from undersampled data. The cleaned k-space is then reconstructed with standard SENSE, avoiding the prohibitive cost of full Aligned-SENSE. Experiments on highly motion-corrupted 1-mm whole-brain GRE (Tacq=10 min, 1620 trackings) and EPTI (Tacq=2 min, 544 trackings) report accurate reconstructions with negligible time penalty, while Aligned-SENSE requires >10 h and >10 days respectively.

Significance. If the kernels produce data whose only remaining corruptions are coil sensitivities and undersampling, the approach would enable routine incorporation of high-temporal-resolution motion and dB0 tracking into parallel imaging without new artifacts or excessive compute. The reported experiments on two sequences with hundreds of motion trackings and the dramatic speed gains constitute a practical strength for motion-robust high-resolution MRI.

major comments (2)

[Abstract] Abstract: the claim of 'accurate reconstruction' is unsupported by any quantitative image-quality metrics (SSIM, NRMSE, etc.), error bars, data-consistency residuals before/after cleaning, or direct visual comparisons to Aligned-SENSE or motion-free references; this directly limits verification that the MLP-generated kernels leave data suitable for artifact-free standard SENSE.
[Methods] The central assumption that local linear GRAPPA operators can exactly compensate for motion/dB0 phase accrual (including potential non-local effects from through-slice or non-rigid motion) is not tested with an explicit residual-artifact or data-consistency analysis; without such a check the claim that standard SENSE then yields images free of correction-induced artifacts remains unverified.

minor comments (1)

[Abstract] Abstract: acquisition parameters (resolution, number of coils, exact undersampling factors) could be stated more explicitly to allow immediate assessment of the experimental setup.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which highlight important aspects of validation and assumptions in our work. We address each major comment below with clarifications and proposed revisions to improve the manuscript.

read point-by-point responses

Referee: [Abstract] Abstract: the claim of 'accurate reconstruction' is unsupported by any quantitative image-quality metrics (SSIM, NRMSE, etc.), error bars, data-consistency residuals before/after cleaning, or direct visual comparisons to Aligned-SENSE or motion-free references; this directly limits verification that the MLP-generated kernels leave data suitable for artifact-free standard SENSE.

Authors: We agree that the abstract would benefit from explicit quantitative support. In the revised manuscript, we will incorporate SSIM and NRMSE metrics (with error bars across slices or subjects) comparing Mobile-GRAPPA reconstructions to motion-free references, along with data-consistency residuals before and after k-space cleaning. Visual comparisons to motion-free data are already shown in the results figures for both GRE and EPTI; we will reference these more directly. Full quantitative comparison to Aligned-SENSE remains limited by its prohibitive runtime (>10 h and >10 days), but we retain the side-by-side qualitative demonstrations where partial Aligned-SENSE runs were feasible. revision: yes
Referee: [Methods] The central assumption that local linear GRAPPA operators can exactly compensate for motion/dB0 phase accrual (including potential non-local effects from through-slice or non-rigid motion) is not tested with an explicit residual-artifact or data-consistency analysis; without such a check the claim that standard SENSE then yields images free of correction-induced artifacts remains unverified.

Authors: The Mobile-GRAPPA design treats motion and dB0 phase as locally correctable via position-specific GRAPPA kernels trained on the tracked parameters. To verify this, the revision will add an explicit data-consistency analysis: we will report the residual norm between the cleaned k-space and the forward model (coil sensitivities and undersampling) used by standard SENSE, demonstrating that correction-induced artifacts are negligible. Regarding non-local effects, our current experiments rely on rigid-body tracking with high temporal resolution (1620 and 544 points); we will add a limitations paragraph acknowledging that through-slice or non-rigid motion may introduce residual errors not fully captured by local linear operators, while noting that the reported high-quality results suggest practical robustness for the tested rigid-dominant cases. revision: partial

Circularity Check

0 steps flagged

No circularity: Mobile-GRAPPA is a trained correction operator whose output is not forced by construction

full rationale

The paper trains an MLP to produce k-space-position-specific GRAPPA kernels from motion- and dB0-tracked data, applies those kernels as a cleaning step, and then feeds the result to standard SENSE. No equation in the provided text equates the final image directly to the fitted kernels or to the original corrupted measurements by algebraic identity. The training step is a conventional supervised mapping whose success is claimed to be validated by downstream image quality rather than by tautological re-use of the same data as both input and output. No self-citation is invoked as a uniqueness theorem or ansatz that would render the choice of MLP or GRAPPA form mandatory. The derivation therefore remains self-contained and does not reduce the claimed reconstruction to a renaming or re-fitting of its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on standard parallel-imaging assumptions that local GRAPPA kernels can model and subtract smooth phase errors, plus the empirical claim that an MLP can learn these kernels efficiently from motion-tracked data.

axioms (1)

domain assumption Local GRAPPA operators trained on motion-tracked data can accurately represent and remove motion-induced and dB0-induced phase errors across k-space.
Invoked when the paper states that the kernels remove corruption so standard SENSE can be used.

pith-pipeline@v0.9.0 · 5551 in / 1361 out tokens · 42274 ms · 2026-05-18T00:02:29.750285+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We efficiently train a family of k-space-position-specific Mobile-GRAPPA kernels via a lightweight multilayer perceptron (MLP) and apply them across k-space to generate clean data.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Mobile-GRAPPA enables accurate reconstruction with negligible time penalty, whereas full Aligned-SENSE was impractical

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

18 extracted references · 18 canonical work pages

[1]

Department of Electrical Engineering, Stanford University, Stanford, CA, USA

work page
[2]

Department of Radiology, Stanford University, Stanford, CA, USA

work page
[3]

cleaning

Siemens Medical Solutions USA, Inc., Malvern, USA Abstract Purpose: Advanced motion-navigations are now enabling rapid-tracking of subject’s motion and dB0-phase, but accurately incorporating such information into SENSE (Aligned- SENSE) can be computationally prohibitive. Mobile-GRAPPA is proposed to provide a motion-and-dB0-phase “cleaning” approach in k...

work page
[4]

Servo navigators: linear regression and feedback control for rigid‐body motion correction[J]

Ulrich T, Riedel M, Pruessmann K P. Servo navigators: linear regression and feedback control for rigid‐body motion correction[J]. Magnetic Resonance in Medicine, 2024, 91(5): 1876-1892. https://doi.org/10.1002/mrm.29967

work page doi:10.1002/mrm.29967 2024
[5]

Rapid and accurate navigators for motion and B 0 tracking using QUEEN: Quantitatively enhanced parameter estimation from navigators[J]

Brackenier Y, Wang N, Liao C, et al. Rapid and accurate navigators for motion and B 0 tracking using QUEEN: Quantitatively enhanced parameter estimation from navigators[J]. Magnetic Resonance in Medicine, 2024, 91(5): 2028 -2043. https://doi.org/10.1002/mrm.29976

work page doi:10.1002/mrm.29976 2024
[6]

Scout accelerated motion estimation and reduction (SAMER)[J]

Polak D, Splitthoff D N, Clifford B, et al. Scout accelerated motion estimation and reduction (SAMER)[J]. Magnetic resona nce in medicine, 2022, 87(1): 163-178. https://doi.org/10.1002/mrm.28971

work page doi:10.1002/mrm.28971 2022
[7]

Scout-based Multi-Echo NAvigating (SMENA) for high temporal resolution motion and B0 estimation: applications to EPTI and multi-echo GRE[J]

Wang N, Brackenier Y, Nurdinova A, et al. Scout-based Multi-Echo NAvigating (SMENA) for high temporal resolution motion and B0 estimation: applications to EPTI and multi-echo GRE[J]

work page
[8]

Effect of head motion on MRI B 0 field distribution[J]

Liu J, de Zwart J A, van Gelderen P, et al. Effect of head motion on MRI B 0 field distribution[J]. Magnetic resonance in medicine, 2018, 80(6): 2538-2548. https://doi.org/10.1002/mrm.27339

work page doi:10.1002/mrm.27339 2018
[9]

Sensitivity encoding for aligned multishot magnetic resonance reconstruction[J]

Cordero -Grande L, Teixeira R P A G, Hughes E J, et al. Sensitivity encoding for aligned multishot magnetic resonance reconstruction[J]. IEEE Transactions on Computational Imaging, 2016, 2(3): 266-280. doi: 10.1109/TCI.2016.2557069

work page doi:10.1109/tci.2016.2557069 2016
[10]

Echo planar time‐resolved imaging (EPTI)[J]

Wang F, Dong Z, Reese T G, et al. Echo planar time‐resolved imaging (EPTI)[J]. Magnetic resonance in medicine, 2019, 81(6): 3599-3615. https://doi.org/10.1002/mrm.27673

work page doi:10.1002/mrm.27673 2019
[11]

Echo planar time‐resolved imaging with subspace reconstruction and optimized spatiotemporal encoding[J]

Dong Z, Wang F, Reese T G, et al. Echo planar time‐resolved imaging with subspace reconstruction and optimized spatiotemporal encoding[J]. Magnetic resonance in medicine, 2020, 84(5): 2442-2455. https://doi.org/10.1002/mrm.28295

work page doi:10.1002/mrm.28295 2020
[12]

Augmented generalized SENSE reconstruction to correct for rigid body motion[J]

Bammer R, Aksoy M, Liu C. Augmented generalized SENSE reconstruction to correct for rigid body motion[J]. Magnetic Resonance in Medicine, 2007, 57(1): 90-102. https://doi.org/10.1002/mrm.21106

work page doi:10.1002/mrm.21106 2007
[13]

Correction of B0 -induced geometric distortion variations in prospective motion correction for 7T MRI[J]

Yarach U, Luengviriya C, Stucht D, et al. Correction of B0 -induced geometric distortion variations in prospective motion correction for 7T MRI[J]. Magnetic Resonance Materials in Physics, Biology and Medicine, 2016, 29(3): 319 -332. https://doi.org/10.1007/s10334-015-0515-2

work page doi:10.1007/s10334-015-0515-2 2016
[14]

Fast and accurate motion-corrected reconstruction with motion-correcting Implicit GROG (motion-iGROG)[J]

Lin Y, Abraham D, Wang N, et al. Fast and accurate motion-corrected reconstruction with motion-correcting Implicit GROG (motion-iGROG)[J]

work page
[15]

Implicit Representation of GRAPPA Kernels for Fast MRI Reconstruction[J]

Abraham D, Nishimura M, Cao X, et al. Implicit Representation of GRAPPA Kernels for Fast MRI Reconstruction[J]. arXiv preprint arXiv:2310.10823, 2023

work page arXiv 2023
[16]

In vivo B0 field shimming methods for MRI at 7 T[J]

Stockmann J P, Wald L L. In vivo B0 field shimming methods for MRI at 7 T[J]. Neuroimage, 2018, 168: 71 -87. https://doi.org/10.1016/j.neuroimage.2017.06.013

work page doi:10.1016/j.neuroimage.2017.06.013 2018
[17]

Some methods of classification and analysis of multivariate observations[C]//Proc

McQueen J B. Some methods of classification and analysis of multivariate observations[C]//Proc. of 5th Berkeley Symposium on Math. Stat. and Prob. 1967: 281-297

work page 1967
[18]

k-means++: The advantages of careful seeding[R]

Arthur D, Vassilvitskii S. k-means++: The advantages of careful seeding[R]. Stanford, 2006. Figure 1 (A) Aligned-SENSE with modified forward operator to account for motion-related effects. (B) Application of Mobile-GRAPPA kernels (G) to clean motion-corrupted data. (C) MLP architecture for efficient GRAPPA kernel training and compact storage. (D) Motion-c...

work page 2006

[1] [1]

Department of Electrical Engineering, Stanford University, Stanford, CA, USA

work page

[2] [2]

Department of Radiology, Stanford University, Stanford, CA, USA

work page

[3] [3]

cleaning

Siemens Medical Solutions USA, Inc., Malvern, USA Abstract Purpose: Advanced motion-navigations are now enabling rapid-tracking of subject’s motion and dB0-phase, but accurately incorporating such information into SENSE (Aligned- SENSE) can be computationally prohibitive. Mobile-GRAPPA is proposed to provide a motion-and-dB0-phase “cleaning” approach in k...

work page

[4] [4]

Servo navigators: linear regression and feedback control for rigid‐body motion correction[J]

Ulrich T, Riedel M, Pruessmann K P. Servo navigators: linear regression and feedback control for rigid‐body motion correction[J]. Magnetic Resonance in Medicine, 2024, 91(5): 1876-1892. https://doi.org/10.1002/mrm.29967

work page doi:10.1002/mrm.29967 2024

[5] [5]

Rapid and accurate navigators for motion and B 0 tracking using QUEEN: Quantitatively enhanced parameter estimation from navigators[J]

Brackenier Y, Wang N, Liao C, et al. Rapid and accurate navigators for motion and B 0 tracking using QUEEN: Quantitatively enhanced parameter estimation from navigators[J]. Magnetic Resonance in Medicine, 2024, 91(5): 2028 -2043. https://doi.org/10.1002/mrm.29976

work page doi:10.1002/mrm.29976 2024

[6] [6]

Scout accelerated motion estimation and reduction (SAMER)[J]

Polak D, Splitthoff D N, Clifford B, et al. Scout accelerated motion estimation and reduction (SAMER)[J]. Magnetic resona nce in medicine, 2022, 87(1): 163-178. https://doi.org/10.1002/mrm.28971

work page doi:10.1002/mrm.28971 2022

[7] [7]

Scout-based Multi-Echo NAvigating (SMENA) for high temporal resolution motion and B0 estimation: applications to EPTI and multi-echo GRE[J]

Wang N, Brackenier Y, Nurdinova A, et al. Scout-based Multi-Echo NAvigating (SMENA) for high temporal resolution motion and B0 estimation: applications to EPTI and multi-echo GRE[J]

work page

[8] [8]

Effect of head motion on MRI B 0 field distribution[J]

Liu J, de Zwart J A, van Gelderen P, et al. Effect of head motion on MRI B 0 field distribution[J]. Magnetic resonance in medicine, 2018, 80(6): 2538-2548. https://doi.org/10.1002/mrm.27339

work page doi:10.1002/mrm.27339 2018

[9] [9]

Sensitivity encoding for aligned multishot magnetic resonance reconstruction[J]

Cordero -Grande L, Teixeira R P A G, Hughes E J, et al. Sensitivity encoding for aligned multishot magnetic resonance reconstruction[J]. IEEE Transactions on Computational Imaging, 2016, 2(3): 266-280. doi: 10.1109/TCI.2016.2557069

work page doi:10.1109/tci.2016.2557069 2016

[10] [10]

Echo planar time‐resolved imaging (EPTI)[J]

Wang F, Dong Z, Reese T G, et al. Echo planar time‐resolved imaging (EPTI)[J]. Magnetic resonance in medicine, 2019, 81(6): 3599-3615. https://doi.org/10.1002/mrm.27673

work page doi:10.1002/mrm.27673 2019

[11] [11]

Echo planar time‐resolved imaging with subspace reconstruction and optimized spatiotemporal encoding[J]

Dong Z, Wang F, Reese T G, et al. Echo planar time‐resolved imaging with subspace reconstruction and optimized spatiotemporal encoding[J]. Magnetic resonance in medicine, 2020, 84(5): 2442-2455. https://doi.org/10.1002/mrm.28295

work page doi:10.1002/mrm.28295 2020

[12] [12]

Augmented generalized SENSE reconstruction to correct for rigid body motion[J]

Bammer R, Aksoy M, Liu C. Augmented generalized SENSE reconstruction to correct for rigid body motion[J]. Magnetic Resonance in Medicine, 2007, 57(1): 90-102. https://doi.org/10.1002/mrm.21106

work page doi:10.1002/mrm.21106 2007

[13] [13]

Correction of B0 -induced geometric distortion variations in prospective motion correction for 7T MRI[J]

Yarach U, Luengviriya C, Stucht D, et al. Correction of B0 -induced geometric distortion variations in prospective motion correction for 7T MRI[J]. Magnetic Resonance Materials in Physics, Biology and Medicine, 2016, 29(3): 319 -332. https://doi.org/10.1007/s10334-015-0515-2

work page doi:10.1007/s10334-015-0515-2 2016

[14] [14]

Fast and accurate motion-corrected reconstruction with motion-correcting Implicit GROG (motion-iGROG)[J]

Lin Y, Abraham D, Wang N, et al. Fast and accurate motion-corrected reconstruction with motion-correcting Implicit GROG (motion-iGROG)[J]

work page

[15] [15]

Implicit Representation of GRAPPA Kernels for Fast MRI Reconstruction[J]

Abraham D, Nishimura M, Cao X, et al. Implicit Representation of GRAPPA Kernels for Fast MRI Reconstruction[J]. arXiv preprint arXiv:2310.10823, 2023

work page arXiv 2023

[16] [16]

In vivo B0 field shimming methods for MRI at 7 T[J]

Stockmann J P, Wald L L. In vivo B0 field shimming methods for MRI at 7 T[J]. Neuroimage, 2018, 168: 71 -87. https://doi.org/10.1016/j.neuroimage.2017.06.013

work page doi:10.1016/j.neuroimage.2017.06.013 2018

[17] [17]

Some methods of classification and analysis of multivariate observations[C]//Proc

McQueen J B. Some methods of classification and analysis of multivariate observations[C]//Proc. of 5th Berkeley Symposium on Math. Stat. and Prob. 1967: 281-297

work page 1967

[18] [18]

k-means++: The advantages of careful seeding[R]

Arthur D, Vassilvitskii S. k-means++: The advantages of careful seeding[R]. Stanford, 2006. Figure 1 (A) Aligned-SENSE with modified forward operator to account for motion-related effects. (B) Application of Mobile-GRAPPA kernels (G) to clean motion-corrupted data. (C) MLP architecture for efficient GRAPPA kernel training and compact storage. (D) Motion-c...

work page 2006