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arxiv: 2604.09233 · v1 · submitted 2026-04-10 · 📡 eess.IV

Recognition: no theorem link

A GPU-enhanced workflow for non-Fourier SENSE reconstruction

Samuel Bianchi , Klaas P. Pruessmann
Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:19 UTC · model grok-4.3

classification 📡 eess.IV
keywords non-Fourier SENSEGPU reconstructionspiral trajectoryB0 off-resonancecoil sensitivityMRI image reconstructionundersampled data
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The pith

A GPU implementation makes non-Fourier SENSE reconstruction feasible for long-readout spiral MRI data.

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

The paper develops a workflow for mapping coil sensitivities and B0 off-resonance fields to support non-Fourier SENSE reconstruction in MRI. This reconstruction method is necessary when data from spiral trajectories with long readouts and B0 effects cannot be handled by standard FFT-based methods. An implementation optimized for GPU execution is provided and tested on 2D and 3D spiral datasets with readouts up to 71.5 milliseconds and undersampling up to factor 7. The work shows that runtimes become practical with GPU acceleration and emphasizes correct stopping to avoid artifacts. All components are released as open code.

Core claim

The authors provide an efficient GPU implementation of non-Fourier SENSE that incorporates full signal models for sensitivities and B0, achieving high performance on spiral data with extended readout durations and high acceleration factors, with practical runtimes and robust mapping workflow.

What carries the argument

The non-Fourier SENSE iterative reconstruction algorithm, accelerated on GPU via selective use of the FFT, supported by a pipeline for accurate coil sensitivity and B0 field mapping.

If this is right

  • Reconstruction of highly undersampled spiral data with long readouts becomes computationally viable.
  • GPU acceleration significantly reduces the time needed compared to CPU-only versions.
  • Careful choice of stopping criteria is required to maintain image quality without introducing artifacts.
  • Open availability of the code allows direct use and adaptation in other research settings.

Where Pith is reading between the lines

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

  • Similar workflows could be adapted for other non-Cartesian k-space trajectories.
  • Real-time or online reconstruction pipelines might benefit from this GPU approach.
  • Further optimizations could target even longer readouts or higher dimensions.

Load-bearing premise

The non-Fourier signal model along with the calculated sensitivity and B0 maps must faithfully capture the actual physical signal acquisition so the solver yields clean images.

What would settle it

If reconstructed images from the 2D or 3D spiral test datasets exhibit uncorrectable artifacts even at optimal stopping points, or if they deviate substantially from known reference reconstructions, the performance claim would be undermined.

Figures

Figures reproduced from arXiv: 2604.09233 by Klaas P. Pruessmann, Samuel Bianchi.

Figure 1
Figure 1. Figure 1: Overview of all the necessary data and processing steps for non-Fourier SENSE reconstruction. Prescan data are used to compute a trusted mask (MT , blue) and a reconstruction mask (MR, red). The trusted mask contains all voxels with a sufficiently high signal-to-noise ratio (SNR) to compute sensitivity maps Sλ, and the reconstruction mask contains all voxels where signal sources (spins) may have been prese… view at source ↗
Figure 2
Figure 2. Figure 2: Top-left: Non-Fourier SENSE reconstruction if enough memory for all arrays is available. Top-right: Column-major non-Fourier SENSE reconstruction if not enough memory for the matrix P is available. All other arrays are expected to fit into memory. Bottom-left: Descriptive information for both algorithms. Bottom-right: Necessary adaptions of the column-major non-Fourier SENSE reconstruction for an implement… view at source ↗
Figure 3
Figure 3. Figure 3: Single-shot 2D spiral images. FOV: 219x219x36mm, Resolution: 1x1x2mm, Slice gap: 0mm, R = 2, 3, 4, 5, 6, TE = 30ms, TAq = 71.5ms, 47.7ms, 35.8ms, 28.7ms, 24ms, Number of CG iterations: 7, 13, 16, 26, 46. Reference images from a spin-warp scan are shown at the bottom row for comparison. 23 / 31 [PITH_FULL_IMAGE:figures/full_fig_p024_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: 3D T-Hex spiral images. FOV: 219x219x36mm, Resolution: 1x1x2mm, R = 3, 4, 5, 6, 7, TE = 30ms, TR = 250ms, TAq = 67.1ms, 58.2ms, 52.1ms, 47.6ms, 44.1ms, Number of CG iterations: 47, 37, 46, 50, 56. Reference images from a spin-warp scan are shown at the bottom row for comparison. 24 / 31 [PITH_FULL_IMAGE:figures/full_fig_p025_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Influence of higher-order field terms on non-Fourier SENSE reconstruction. Top row: Re￾construction results when using field terms up to 3rd-order for the 2D and 3D spiral datasets. Bottom row: Equivalent results when using field terms up to 1st-order. 25 / 31 [PITH_FULL_IMAGE:figures/full_fig_p026_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Top row: L-curves (250 CG iterations) for the reconstruction of 1 slice of the 2D spiral dataset and the reconstruction of the 3D spiral dataset. Arrows indicate in which direction the L-curve is traversed over the CG iterations. Crosses indicate when visual inspection suggest good image quality. Middle row: Evolution of SSIM, for both datasets, over 250 CG iterations. The reference image shown on the bott… view at source ↗
Figure 7
Figure 7. Figure 7: Influence of sensitivity map (Sλ) -processing on non-Fourier SENSE reconstruction. Top row: Sensitivity maps of all 16 receiver coils and reconstruction examples after using the suggested smoothing and extrapolation algorithm. Bottom row: Equivalent examples computed without applying the suggested smoothing and extrapolation algorithm. Magnitude and phase of the reconstructed images are shown and compared … view at source ↗
Figure 8
Figure 8. Figure 8: Influence of B0 map-processing on non-Fourier SENSE reconstruction. Top row: B0 maps and reconstruction examples after using the suggested smoothing and extrapolation algorithm. Second row: Equivalent examples computed without any processing of the B0 map. Third row: Equivalent examples computed after smoothing the B0 map with a Gaussian filter. Bottom row: Equivalent exam￾ples computed after removing nois… view at source ↗
Figure 9
Figure 9. Figure 9: Influence of the reconstruction mask (MR) on non-Fourier SENSE reconstruction. For the examples shown, MR, computed as suggested, was shrinked to coincide with the trusted mask (MT ), dilated, and expanded to cover the full field of view (FOV). The corresponding masks are displayed in the left column. The sensitivity maps (Sλ) and B0 maps were computed accordingly and are presented in the second and third … view at source ↗
Figure 10
Figure 10. Figure 10: Influence of the k-space filter (f) on non-Fourier SENSE reconstruction. Left side: Unfiltered k-space content of the reconstructed image. Right side, top row: K-space filter and reconstruction examples after using the suggested computation method. Second row: Equivalent examples computed after dilating the suggested k-space filter. Third row: Equivalent examples computed when not applying the kspace filt… view at source ↗
read the original abstract

Purpose: Image reconstruction in challenging scenarios requires accurate characterisations of coil sensitivity profiles, local off-resonances (B0) and effective encoding fields. Reconstruction methods utilising all of this information rely on signal models that are not compatible with the classical Fourier/k-space interpretation of the coil data. Hence, the FFT and related techniques are no more applicable, rendering image reconstruction computationally demanding. Methods: This article contains a workflow for accurate sensitivity and B0 mapping as well as other required processing steps. An implementation of non-Fourier SENSE reconstruction is provide that is well suited for execution on a GPU using the FFT. Important practical aspects like stopping criteria and sources of image artifacts are analyzed and documented. Results: Highly performant image reconstruction could be demonstrated on a 2D and 3D spiral dataset. These datasets contain trajectories featuring readout durations up to 71.5ms and undersampling factors up to R = 7. Running the reconstruction on a GPU greatly boosts reconstruction speed. Stopping the reconstruction at the right moment is crucial for image quality. All methods included in this article are available in a public code repository. Conclusion: The provided implementation of non-Fourier SENSE reconstruction is highly performant. When it is executed on GPU, runtimes reach a duration feasible in practice. The presented workflow ensures robust and accurate computation of coil sensitive profiles and off-resonance maps.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The manuscript describes a complete workflow for non-Fourier SENSE MRI reconstruction, including methods for computing coil sensitivity profiles and B0 off-resonance maps, an iterative solver implementation optimized for GPU execution via FFT, analysis of stopping criteria and artifact sources, and demonstration on 2D and 3D spiral k-space trajectories with readout durations up to 71.5 ms and acceleration factors up to R=7. The code is made publicly available.

Significance. If the results hold, this work provides a practical, GPU-accelerated solution for high-performance image reconstruction in challenging non-Cartesian MRI scenarios where standard FFT-based methods fail. The public code repository is a strength, enabling reproducibility and further development. The analysis of practical aspects like stopping criteria adds value for users.

major comments (2)
  1. [Abstract and Results] Abstract and Results: The claims of 'highly performant' reconstruction and 'robust and accurate' mapping are not supported by quantitative error metrics (e.g., RMSE or SSIM relative to a reference image), direct comparisons to alternative reconstructions, or numerical runtime benchmarks with and without GPU acceleration.
  2. [Methods] Methods: No explicit description or validation (e.g., phantom-based checks or consistency metrics) is given for the accuracy of the computed sensitivity profiles and B0 maps, which is central to the assumption that the non-Fourier signal model accurately describes the acquisition.
minor comments (2)
  1. [Abstract] The abstract would benefit from inclusion of at least one concrete runtime or speedup value to quantify the GPU advantage.
  2. [Figures] Figure legends and dataset descriptions could be expanded to clarify the exact spiral trajectories, coil counts, and field strengths used in the demonstrations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive review and recommendation for minor revision. We address each major comment below, indicating the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract and Results] Abstract and Results: The claims of 'highly performant' reconstruction and 'robust and accurate' mapping are not supported by quantitative error metrics (e.g., RMSE or SSIM relative to a reference image), direct comparisons to alternative reconstructions, or numerical runtime benchmarks with and without GPU acceleration.

    Authors: We agree that quantitative metrics would provide stronger support for the performance claims. The current results emphasize practical demonstration on challenging long-readout spiral data with high acceleration. In the revision we will add runtime benchmarks (GPU versus CPU) and error metrics such as RMSE or SSIM against a reference reconstruction where a suitable reference is available from the datasets, along with brief comparisons to alternative reconstruction approaches. revision: yes

  2. Referee: [Methods] Methods: No explicit description or validation (e.g., phantom-based checks or consistency metrics) is given for the accuracy of the computed sensitivity profiles and B0 maps, which is central to the assumption that the non-Fourier signal model accurately describes the acquisition.

    Authors: The Methods section outlines the sensitivity and B0 mapping workflow using established techniques, but we acknowledge that additional explicit description and validation would improve clarity. We will expand the description of these steps and incorporate consistency metrics or cross-validation checks on the provided in vivo datasets to better substantiate map accuracy. revision: yes

Circularity Check

0 steps flagged

No significant circularity in implementation workflow

full rationale

The paper is an engineering and implementation description of a GPU-accelerated non-Fourier SENSE workflow, including sensitivity/B0 mapping, iterative solver details, stopping criteria, and artifact analysis. It demonstrates feasible runtimes and image quality on provided 2D/3D spiral datasets (readouts to 71.5 ms, R=7) via public code, but makes no first-principles derivations, predictions, or uniqueness claims that reduce by construction to quantities fitted from the same data. All load-bearing steps are explicit processing choices and empirical checks external to any self-referential loop; the model-accuracy assumption is the standard one for such reconstructions and is addressed by documented validation rather than by definition.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper is an engineering implementation that relies on established MRI forward models and numerical optimization rather than introducing new theory or fitted constants.

axioms (1)
  • domain assumption The non-Fourier signal model accurately captures coil sensitivities, B0 offsets, and encoding fields in the acquired data
    Invoked throughout the reconstruction workflow and GPU implementation description.

pith-pipeline@v0.9.0 · 5544 in / 1255 out tokens · 53288 ms · 2026-05-10T17:19:15.072582+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

71 extracted references · 60 canonical work pages

  1. [1]

    H. S. Abdul-Rahman, M. A. Gdeisat, D. R. Burton, M. J. Lalor, F. Lilley, and C. J. Moore. Fast and robust three-dimensional best path phase unwrapping algorithm.Applied Optics, 46(26):6623–6635,

  2. [2]

    doi: doi.org/10.1364/AO.46.006623

    work page doi:10.1364/ao.46.006623

  3. [3]

    C. B. Ahn, J. H. Kim, and Z. H. Cho. High-speed spiral-scan echo planar nmr imaging-i.IEEE Transactions on Medical Imaging, 5(1):2–7, 1986. doi: doi.org/10.1109/TMI.1986.4307732

    work page doi:10.1109/tmi.1986.4307732 1986

  4. [4]

    J. L. R. Andersson, S. Skare, and J. Ashburner. How to correct susceptibility distortions in spin-echo echo-planar images: application to diffusion tensor imaging.NeuroImage, 20(2):870–888, 2003. doi: doi.org/10.1016/S1053-8119(03)00336-7

    work page doi:10.1016/s1053-8119(03)00336-7 2003

  5. [5]

    Ashburner and K

    J. Ashburner and K. J. Friston. Unified segmentation.NeuroImage, 26(3):839–851, 2005. doi: doi.org/10.1016/j.neuroimage.2005.02.018

    work page doi:10.1016/j.neuroimage.2005.02.018 2005

  6. [6]

    Barmet, J

    C. Barmet, J. Tsao, and K. P. Pruessmann. Sensitivity encoding and b0 inhomogeneity - a simul- taneous reconstruction approach.Proceedings of the International Society for Magnetic Resonance in Medicine 13, page 682, 2005

    2005

  7. [7]

    Barmet, N

    C. Barmet, N. De Zanche, and K. P. Pruessmann. Spatiotemporal magnetic field monitoring for mr.Magnetic Resonance in Medicine, 60(1):187–197, 2008. doi: doi.org/10.1002/mrm.21603

    work page doi:10.1002/mrm.21603 2008

  8. [8]

    Bianchi.Advancements in Functional Magnetic Resonance Imaging: Reconstruction, Modeling, and Analysis

    S. Bianchi.Advancements in Functional Magnetic Resonance Imaging: Reconstruction, Modeling, and Analysis. PhD thesis, 2025

    2025

  9. [9]

    Blaimer, F

    M. Blaimer, F. Breuer, M. Mueller, R. M. Heidemann, M. A. Griswold, and P. M. Jakob. Smash, sense, pils, grappa: how to choose the optimal method.Topics in magnetic resonance imaging, 15 (4):223–236, 2004. doi: doi.org/10.1097/01.rmr.0000136558.09801.dd

    work page doi:10.1097/01.rmr.0000136558.09801.dd 2004

  10. [10]

    K. T. Block and J. Frahm. Spiral imaging: a critical appraisal.Journal of magnetic resonance imaging, 21(6):657–668, 2005. doi: doi.org/10.1002/jmri.20320

    work page doi:10.1002/jmri.20320 2005

  11. [11]

    D. O. Brunner and K. P. Pruessmann. Svd analysis of array transmission and reception and its use for bootstrapping calibration.Magnetic Resonance in Medicine, 76(6):1730–1740, 2016. ISSN 0740-3194. doi: doi.org/10.1002/mrm.26060

    work page doi:10.1002/mrm.26060 2016

  12. [12]

    B¨ ornert, H

    P. B¨ ornert, H. Schomberg, B. Aldefeld, and J. Groen. Improvements in spiral mr imaging.Magnetic Resonance Materials in Physics, Biology and Medicine, 9(1):29–41, 1999. doi: doi.org/10.1007/ BF02634590

    1999

  13. [13]

    R. W. Chan, C. von Deuster, D. Giese, C. T. Stoeck, J. Harmer, A. P. Aitken, D. Atkinson, and S. Kozerke. Characterization and correction of eddy-current artifacts in unipolar and bipolar diffusion sequences using magnetic field monitoring.Journal of Magnetic Resonance, 244:74–84,

  14. [14]

    doi: doi.org/10.1016/j.jmr.2014.04.018

    work page doi:10.1016/j.jmr.2014.04.018 2014

  15. [15]

    Chauffert, P

    N. Chauffert, P. Ciuciu, J. Kahn, and P. Weiss. Variable density sampling with continuous trajec- tories.SIAM Journal on Imaging Sciences, 7(4):1962–1992, 2014. doi: doi.org/10.1137/130946642. 14 / 31 A GPU-enhanced workflow for non-Fourier SENSE reconstruction BIANCHI et al

    work page doi:10.1137/130946642 1962

  16. [16]

    B. Dale, M. Wendt, and J. L. Duerk. A rapid look-up table method for reconstructing mr images from arbitrary k-space trajectories.IEEE Transactions on Medical Imaging, 20(3):207–217, 2001. doi: doi.org/10.1109/42.918471

    work page doi:10.1109/42.918471 2001

  17. [17]

    Deshmane, V

    A. Deshmane, V. Gulani, M. A. Griswold, and N. Seiberlich. Parallel mr imaging.Journal of Magnetic Resonance Imaging, 36(1):55–72, 2012. doi: doi.org/10.1002/jmri.23639

    work page doi:10.1002/jmri.23639 2012

  18. [18]

    B. E. Dietrich, D. O. Brunner, B. J. Wilm, C. Barmet, S. Gross, L. Kasper, M. Haeberlin, T. Schmid, S. J. Vannesjo, and K. P. Pruessmann. A field camera for mr sequence monitoring and system analysis.Magnetic Resonance in Medicine, 75(4):1831–1840, 2016. doi: doi.org/10.1002/mrm.25770

    work page doi:10.1002/mrm.25770 2016

  19. [19]

    Dymerska, K

    B. Dymerska, K. Eckstein, B. Bachrata, B. Siow, S. Trattnig, K. Shmueli, and S. D. Robinson. Phase unwrapping with a rapid opensource minimum spanning tree algorithm (romeo).Magnetic Resonance in Medicine, 85(4):2294–2308, 2021. doi: doi.org/10.1002/mrm.28563

    work page doi:10.1002/mrm.28563 2021

  20. [20]

    W. A. Edelstein, J. M. Hutchison, G. Johnson, and T. Redpath. Spin warp nmr imaging and applications to human whole-body imaging.Physics in Medicine & Biology, 25(4):751–756, 1980. doi: doi.org/10.1088/0031-9155/25/4/017

    work page doi:10.1088/0031-9155/25/4/017 1980

  21. [21]

    Engel, L

    M. Engel, L. Kasper, C. Barmet, T. Schmid, L. Vionnet, B. Wilm, and K. P. Pruessmann. Single- shot spiral imaging at 7 t.Magnetic Resonance in Medicine, 80(5):1836–1846, 2018. doi: doi.org/ 10.1002/mrm.27176

    work page doi:10.1002/mrm.27176 2018

  22. [22]

    Engel, L

    M. Engel, L. Kasper, B. Wilm, B. Dietrich, L. Vionnet, F. Hennel, J. Reber, and K. P. Pruessmann. T-hex: Tilted hexagonal grids for rapid 3d imaging.Magnetic Resonance in Medicine, 85(5):2507– 2523, 2021. doi: doi.org/10.1002/mrm.28600

    work page doi:10.1002/mrm.28600 2021

  23. [23]

    J. F. Glockner, H. H. Hu, D. W. Stanley, L. Angelos, and K. King. Parallel mr imaging: a user’s guide.Radiographics, 25(5):1279–1297, 2005. doi: doi.org/10.1148/rg.255045202

    work page doi:10.1148/rg.255045202 2005

  24. [24]

    G. H. Glover. Spiral imaging in fmri.NeuroImage, 62(2):706–712, 2012. doi: doi.org/10.1016/j. neuroimage.2011.10.039

    work page doi:10.1016/j 2012

  25. [25]

    G. H. Glover and S. Lai. Self-navigated spiral fmri: Interleaved versus single-shot.Magnetic Resonance in Medicine, 39(3):361–368, 1998. doi: doi.org/10.1002/mrm.1910390305

    work page doi:10.1002/mrm.1910390305 1998

  26. [26]

    M. A. Griswold, P. M. Jakob, M. Nittka, J. W. Goldfarb, and A. Haase. Partially parallel imaging with localized sensitivities (pils).Magnetic Resonance in Medicine, 44(4):602–609, 2000. doi: doi. org/10.1002/1522-2594(200010)44:4⟨602::aid-mrm14⟩3.0.co;2-5

    work page doi:10.1002/1522-2594(200010)44:4 2000

  27. [27]

    M. A. Griswold, P. M. Jakob, R. M. Heidemann, M. Nittka, V. Jellus, J. Wang, B. Kiefer, and A. Haase. Generalized autocalibrating partially parallel acquisitions (grappa).Magnetic Resonance in Medicine, 47(6):1202–1210, 2002. doi: doi.org/10.1002/mrm.10171

    work page doi:10.1002/mrm.10171 2002

  28. [28]

    F. E. Gunawan and H. Homma.Conjugate Gradient and L-Curve Like Methods for Large In- verse Problem, pages 283–293. Elsevier Science B.V., Amsterdam, 2003. doi: doi.org/10.1016/ B978-008044268-6/50034-X

    2003

  29. [29]

    Hamilton, D

    J. Hamilton, D. Franson, and N. Seiberlich. Recent advances in parallel imaging for mri.Progress in nuclear magnetic resonance spectroscopy, 101:71–95, 2017. doi: doi.org/10.1016/j.pnmrs.2017. 04.002. 15 / 31 A GPU-enhanced workflow for non-Fourier SENSE reconstruction BIANCHI et al

    work page doi:10.1016/j.pnmrs.2017 2017

  30. [30]

    P. C. Hansen and D. P. O’Leary. The use of the l-curve in the regularization of discrete ill-posed problems.SIAM Journal on Scientific Computing, 14(6):1487–1503, 1993. doi: doi.org/10.1137/ 0914086

    1993

  31. [31]

    Hennel, B

    F. Hennel, B. Wilm, M. B. Roesler, M. Weiger, B. Dietrich, and K. P. Pruessmann. Echo-planar imaging of the human head with 100 mt/m gradients and high-order modeling of eddy current fields. Magnetic Resonance in Medicine, 84(2):751–761, 2020. doi: doi.org/10.1002/mrm.28168

    work page doi:10.1002/mrm.28168 2020

  32. [32]

    M. R. Hestenes and E. Stiefel. Methods of conjugate gradients for solving linear systems.Journal of research of the National Bureau of Standards, 49(6):409–436, 1952. doi: doi.org/10.6028/JRES. 049.044

    work page doi:10.6028/jres 1952

  33. [33]

    Irarrazabal and D

    P. Irarrazabal and D. G. Nishimura. Fast three dimensional magnetic resonance imaging.Magnetic Resonance in Medicine, 33(5):656–662, 1995. doi: doi.org/10.1002/mrm.1910330510

    work page doi:10.1002/mrm.1910330510 1995

  34. [34]

    J. I. Jackson, C. H. Meyer, D. G. Nishimura, and A. Macovski. Selection of a convolution function for fourier inversion using gridding (computerised tomography application).IEEE Transactions on Medical Imaging, 10(3):473–478, 1991. doi: doi.org/10.1109/42.97598

    work page doi:10.1109/42.97598 1991

  35. [35]

    Jenkinson

    M. Jenkinson. Improved unwarping of epi images using regularised b0 maps.NeuroImage, 13(6, Supplement):165, 2001. doi: doi.org/10.1016/S1053-8119(01)91508-3

    work page doi:10.1016/s1053-8119(01)91508-3 2001

  36. [36]

    Jenkinson

    M. Jenkinson. Fast, automated, n-dimensional phase-unwrapping algorithm.Magnetic Resonance in Medicine, 49(1):193–197, 2003. doi: doi.org/10.1002/mrm.10354

    work page doi:10.1002/mrm.10354 2003

  37. [37]

    An analytical solution to the dispersion-by-inversion problem in magnetic resonance elastography.Magnetic Res- onance in Medicine, 84(1):61–71, July 2020

    P. Jezzard and R. S. Balaban. Correction for geometric distortion in echo planar images from b0 field variations.Magnetic Resonance in Medicine, 34(1):65–73, 1995. doi: doi.org/10.1002/mrm. 1910340111

    work page doi:10.1002/mrm 1995

  38. [38]

    K. O. Johnson and J. G. Pipe. Convolution kernel design and efficient algorithm for sampling density correction.Magnetic Resonance in Medicine, 61(2):439–447, 2009. ISSN 0740-3194. doi: doi.org/10.1002/mrm.21840

    work page doi:10.1002/mrm.21840 2009

  39. [39]

    K. J. Layton, D. Gallichan, F. Testud, C. A. Cocosco, A. M. Welz, C. Barmet, K. P. Pruessmann, J. Hennig, and M. Zaitsev. Single shot trajectory design for region-specific imaging using linear and nonlinear magnetic encoding fields.Magnetic Resonance in Medicine, 70(3):684–696, 2013. doi: doi.org/10.1002/mrm.24494

    work page doi:10.1002/mrm.24494 2013

  40. [40]

    R. Ma, M. Ak¸ cakaya, S. Moeller, E. Auerbach, K. U˘ gurbil, and P.-F. Van de Moortele. A field- monitoring-based approach for correcting eddy-current-induced artifacts of up to the 2nd spatial order in human-connectome-project-style multiband diffusion mri experiment at 7t: A pilot study. NeuroImage, 216:116861, 2020. doi: doi.org/10.1016/j.neuroimage.20...

    work page doi:10.1016/j.neuroimage.2020.116861 2020

  41. [41]

    L.-C. Man, J. M. Pauly, and A. Macovski. Multifrequency interpolation for fast off-resonance correction.Magnetic Resonance in Medicine, 37(5):785–792, 1997. ISSN 0740-3194. doi: doi.org/ 10.1002/mrm.1910370523

    work page doi:10.1002/mrm.1910370523 1997

  42. [42]

    N. Otsu. A threshold selection method from gray-level histograms.IEEE Transactions on Systems, Man, and Cybernetics, 9(1):62–66, 1979. doi: doi.org/10.1109/TSMC.1979.4310076. 16 / 31 A GPU-enhanced workflow for non-Fourier SENSE reconstruction BIANCHI et al

    work page doi:10.1109/tsmc.1979.4310076 1979

  43. [43]

    Paquette and T

    E. Paquette and T. Trogdon. Universality for the conjugate gradient and minres algorithms on sample covariance matrices.arXiv, 2020. doi: doi.org/10.48550/arXiv.2007.00640

    work page doi:10.48550/arxiv.2007.00640 2020

  44. [44]

    Patzig.Reconstruction Strategies for MRI in Inhomogeneous Background Fields

    F. Patzig.Reconstruction Strategies for MRI in Inhomogeneous Background Fields. PhD thesis, 2022

    2022

  45. [45]

    J. G. Pipe and P. Menon. Sampling density compensation in mri: Rationale and an iterative numerical solution.Magnetic Resonance in Medicine, 41(1):179–186, 1999. doi: doi.org/10.1002/ (sici)1522-2594(199901)41:1⟨179::Aid-mrm25⟩3.0.Co;2-v

    1999

  46. [46]

    K. P. Pruessmann. Encoding and reconstruction in parallel mri.NMR in biomedicine, 19(3): 288–299, 2006. doi: doi.org/10.1002/nbm.1042

    work page doi:10.1002/nbm.1042 2006

  47. [47]

    K. P. Pruessmann, M. Weiger, M. B. Scheidegger, and P. Boesiger. Sense: Sensitivity encoding for fast mri.Magnetic Resonance in Medicine, 42(5):952–962, 1999. doi: doi.org/10.1002/(SICI) 1522-2594(199911)42:5⟨952::AID-MRM16⟩3.0.CO;2-S

    work page doi:10.1002/(sici 1999

  48. [48]

    K. P. Pruessmann, M. Weiger, P. B¨ ornert, and P. Boesiger. Advances in sensitivity encoding with arbitrary k-space trajectories.Magnetic Resonance in Medicine, 46(4):638–651, 2001. doi: doi.org/10.1002/mrm.1241

    work page doi:10.1002/mrm.1241 2001

  49. [49]

    Robinson, H

    S. Robinson, H. Sch¨ odl, and S. Trattnig. A method for unwrapping highly wrapped multi-echo phase images at very high field: Umpire.Magnetic Resonance in Medicine, 72(1):80–92, 2014. doi: doi.org/10.1002/mrm.24897

    work page doi:10.1002/mrm.24897 2014

  50. [50]

    L. I. Rudin, S. Osher, and E. Fatemi. Nonlinear total variation based noise removal algorithms.Phys- ica D: Nonlinear Phenomena, 60(1):259–268, 1992. doi: doi.org/10.1016/0167-2789(92)90242-F

    work page doi:10.1016/0167-2789(92)90242-f 1992

  51. [51]

    M. A. Schofield and Y. Zhu. Fast phase unwrapping algorithm for interferometric applications. Optics Letters, 28(14):1194–1196, 2003. doi: doi.org/10.1364/OL.28.001194

    work page doi:10.1364/ol.28.001194 2003

  52. [52]

    Schomberg

    H. Schomberg. Off-resonance correction of mr images.IEEE Transactions on Medical Imaging, 18 (6):481–495, 1999. doi: doi.org/10.1109/42.781014

    work page doi:10.1109/42.781014 1999

  53. [53]

    Schomberg and J

    H. Schomberg and J. Timmer. The gridding method for image reconstruction by fourier transforma- tion.IEEE Transactions on Medical Imaging, 14(3):596–607, 1995. doi: doi.org/10.1109/42.414625

    work page doi:10.1109/42.414625 1995

  54. [54]

    Survey over image thresholding techniques and quantitative performance evaluation

    M. Sezgin and B. Sankur. Survey over image thresholding techniques and quantitative performance evaluation.Journal of Electronic Imaging, 13(1):146–165, 2004. doi: doi.org/10.1117/1.1631315

    work page doi:10.1117/1.1631315 2004

  55. [55]

    J. G. Sled, A. P. Zijdenbos, and A. C. Evans. A nonparametric method for automatic correction of intensity nonuniformity in mri data.IEEE Transactions on Medical Imaging, 17(1):87–97, 1998. doi: doi.org/10.1109/42.668698

    work page doi:10.1109/42.668698 1998

  56. [56]

    D. K. Sodickson and W. J. Manning. Simultaneous acquisition of spatial harmonics (smash): fast imaging with radiofrequency coil arrays.Magnetic Resonance in Medicine, 38(4):591–603, 1997. doi: doi.org/10.1002/mrm.1910380414

    work page doi:10.1002/mrm.1910380414 1997

  57. [57]

    Testud, D

    F. Testud, D. Gallichan, K. J. Layton, C. Barmet, A. M. Welz, A. Dewdney, C. A. Cocosco, K. P. Pruessmann, J. Hennig, and M. Zaitsev. Single-shot imaging with higher-dimensional encoding 17 / 31 A GPU-enhanced workflow for non-Fourier SENSE reconstruction BIANCHI et al. using magnetic field monitoring and concomitant field correction.Magnetic Resonance in...

    work page doi:10.1002/mrm.25235 2015

  58. [58]

    R. Tian, M. Uecker, M. Davids, A. Thielscher, K. Buckenmaier, O. Holder, T. Steffen, and K. Schef- fler. Accelerated 2d cartesian mri with an 8-channel local b0 coil array combined with parallel imaging.Magnetic Resonance in Medicine, 91(2):443–465, 2024. doi: doi.org/10.1002/mrm.29799

    work page doi:10.1002/mrm.29799 2024

  59. [59]

    N. J. Tustison, B. B. Avants, P. A. Cook, Y. Zheng, A. Egan, P. A. Yushkevich, and J. C. Gee. N4itk: improved n3 bias correction.IEEE Transactions on Medical Imaging, 29(6):1310–1320, 2010. doi: doi.org/10.1109/tmi.2010.2046908

    work page doi:10.1109/tmi.2010.2046908 2010

  60. [60]

    Murphy, Patrick Virtue, Michael Elad, John M

    M. Uecker, P. Lai, M. J. Murphy, P. Virtue, M. Elad, J. M. Pauly, S. S. Vasanawala, and M. Lustig. Espirit–an eigenvalue approach to autocalibrating parallel mri: where sense meets grappa.Magnetic Resonance in Medicine, 71(3):990–1001, 2014. doi: doi.org/10.1002/mrm.24751

    work page doi:10.1002/mrm.24751 2014

  61. [61]

    Wahlberg, S

    B. Wahlberg, S. Boyd, M. Annergren, and Y. Wang. An admm algorithm for a class of total variation regularized estimation problems*.IFAC Proceedings Volumes, 45(16):83–88, 2012. doi: doi.org/10.3182/20120711-3-BE-2027.00310

    work page doi:10.3182/20120711-3-be-2027.00310 2012

  62. [62]

    2018 , journal =

    M. Weiger, J. Overweg, M. B. R¨ osler, R. Froidevaux, F. Hennel, B. J. Wilm, A. Penn, U. Sturzeneg- ger, W. Schuth, M. Mathlener, M. Borgo, P. B¨ ornert, C. Leussler, R. Luechinger, B. E. Dietrich, J. Reber, D. O. Brunner, T. Schmid, L. Vionnet, and K. P. Pruessmann. A high-performance gra- dient insert for rapid and short-t2 imaging at full duty cycle.Ma...

    work page doi:10.1002/mrm.26954 2018

  63. [63]

    B. J. Wilm, C. Barmet, M. Pavan, and K. P. Pruessmann. Higher order reconstruction for mri in the presence of spatiotemporal field perturbations.Magnetic Resonance in Medicine, 65(6):1690–1701,

  64. [64]

    doi: doi.org/10.1002/mrm.22767

    work page doi:10.1002/mrm.22767

  65. [65]

    B. J. Wilm, C. Barmet, and K. P. Pruessmann. Fast higher-order mr image reconstruction using singular-vector separation.IEEE Transactions on Medical Imaging, 31(7):1396–1403, 2012. doi: doi.org/10.1109/TMI.2012.2190991

    work page doi:10.1109/tmi.2012.2190991 2012

  66. [66]

    B. J. Wilm, C. Barmet, S. Gross, L. Kasper, S. J. Vannesjo, M. Haeberlin, B. E. Dietrich, D. O. Brunner, T. Schmid, and K. P. Pruessmann. Single-shot spiral imaging enabled by an expanded encoding model: Demonstration in diffusion mri.Magnetic Resonance in Medicine, 77(1):83–91,

  67. [67]

    doi: doi.org/10.1002/mrm.26493

    work page doi:10.1002/mrm.26493

  68. [68]

    Advances in Science and Research 17, 143–152

    E. Yudilevich and H. Stark. Spiral sampling in magnetic resonance imaging-the effect of inhomo- geneities.IEEE Transactions on Medical Imaging, 6(4):337–345, 1987. doi: doi.org/10.1109/tmi. 1987.4307852

    work page doi:10.1109/tmi 1987

  69. [69]

    Zahneisen, T

    B. Zahneisen, T. Hugger, K. J. Lee, P. LeVan, M. Reisert, H.-L. Lee, J. Assl¨ ander, M. Zaitsev, and J. Hennig. Single shot concentric shells trajectories for ultra fast fmri.Magnetic Resonance in Medicine, 68(2):484–494, 2012. doi: doi.org/10.1002/mrm.23256

    work page doi:10.1002/mrm.23256 2012

  70. [70]

    W. Zhou, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli. Image quality assessment: from error visibility to structural similarity.IEEE Transactions on Image Processing, 13(4):600–612, 2004. doi: doi.org/10.1109/TIP.2003.819861. 18 / 31 A GPU-enhanced workflow for non-Fourier SENSE reconstruction BIANCHI et al

    work page doi:10.1109/tip.2003.819861 2004

  71. [71]

    N. R. Zwart, K. O. Johnson, and J. G. Pipe. Efficient sample density estimation by combining gridding and an optimized kernel.Magnetic Resonance in Medicine, 67(3):701–10, 2012. doi: doi.org/10.1002/mrm.23041. 19 / 31 A GPU-enhanced workflow for non-Fourier SENSE reconstruction BIANCHI et al. Figures and tables 20 / 31 A GPU-enhanced workflow for non-Four...

    work page doi:10.1002/mrm.23041 2012