DOI: 10.1002/mrm.1120. Direct reconstruction of non‐Cartesian <i>k</i>‐space data using a nonuniform fast Fourier transform

Direct reconstruction of non‐Cartesian k‐space data using a nonuniform fast Fourier transform

10.1002/mrm.1120

Crossref journal-article

Wiley

Magnetic Resonance in Medicine (311)

Abstract

AbstractAn algorithm of Dutt and Rokhlin (SIAM J Sci Comput 1993;14:1368–1383) for the computation of a fast Fourier transform (FFT) of nonuniformly‐spaced data samples has been extended to two dimensions for application to MRI image reconstruction. The 2D nonuniform or generalized FFT (GFFT) was applied to the reconstruction of simulated MRI data collected on radially oriented sinusoidal excursions in k‐space (ROSE) and spiral k‐space trajectories. The GFFT was compared to conventional Kaiser‐Bessel kernel convolution regridding reconstruction in terms of image reconstruction quality and speed of computation. Images reconstructed with the GFFT were similar in quality to the Kaiser‐Bessel kernel reconstructions for 2562 pixel image reconstructions, and were more accurate for smaller 642 pixel image reconstructions. Close inspection of the GFFT reveals it to be equivalent to a convolution regridding method with a Gaussian kernel. The Gaussian kernel had been dismissed in earlier literature as nonoptimal compared to the Kaiser‐Bessel kernel, but a theorem for the GFFT, bounding the approximation error, and the results of the numerical experiments presented here show that this dismissal was based on a nonoptimal selection of Gaussian function. Magn Reson Med 45:908–915, 2001. © 2001 Wiley‐Liss, Inc.

Bibliography

Sarty, G. E., Bennett, R., & Cox, R. W. (2001). Direct reconstruction of nonâCartesian kâspace data using a nonuniform fast Fourier transform. Magnetic Resonance in Medicine, 45(5), 908â915. Portico.

Authors 3

Gordon E. Sarty (first)
Raoqiong Bennett (additional)
Robert W. Cox (additional)

References 18 Referenced 35

10.1109/TMI.1986.4307732
10.1002/mrm.1910280204
10.1002/ima.1850060207
10.1109/42.611345
10.1002/mrm.1910390507
10.1002/1522-2594(200007)44:1<129::AID-MRM19>3.0.CO;2-2
10.1109/42.3926
10.1002/(SICI)1098-1098(1997)8:6<519::AID-IMA4>3.0.CO;2-D
10.1090/S0025-5718-1965-0178586-1
{'key': 'e_1_2_8_11_2', 'volume-title': 'The fast Fourier transform', 'author': 'Brigham EO', 'year': '1974'} / The fast Fourier transform by Brigham EO (1974)
10.1109/42.97598
10.1137/0914081
KannengißerSAR BrennerAR NollTG.Accelerated image reconstruction for sensitivity encoded imaging with arbitraryk‐space trajectories. In: Proceedings of the 8th Annual Meeting of ISMRM Denver 2000. p2967.
10.1118/1.595331
10.1016/0022-2364(83)90060-4
10.1109/42.774166
10.1109/TNS.1974.6499235
{'key': 'e_1_2_8_19_2', 'volume-title': 'Numerical Recipes in C', 'author': 'Press WH', 'year': '1992'} / Numerical Recipes in C by Press WH (1992)

Dates

Type	When
Created	22 years, 11 months ago (Sept. 10, 2002, 6:53 p.m.)
Deposited	1 year, 10 months ago (Oct. 8, 2023, 4:33 p.m.)
Indexed	1 year, 2 months ago (June 6, 2024, 5:22 p.m.)
Issued	24 years, 4 months ago (April 16, 2001)
Published	24 years, 4 months ago (April 16, 2001)
Published Online	24 years, 4 months ago (April 16, 2001)
Published Print	24 years, 3 months ago (May 1, 2001)

Funders 0

None

BibTeX

@article{Sarty_2001, title={Direct reconstruction of non‐Cartesian k‐space data using a nonuniform fast Fourier transform}, volume={45}, ISSN={1522-2594}, url={http://dx.doi.org/10.1002/mrm.1120}, DOI={10.1002/mrm.1120}, number={5}, journal={Magnetic Resonance in Medicine}, publisher={Wiley}, author={Sarty, Gordon E. and Bennett, Raoqiong and Cox, Robert W.}, year={2001}, month=apr, pages={908–915} }

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