Iterative reconstruction of magnetic resonance images from arbitrary samples in k-space

IEEE Transactions on Nuclear Science

Volumn 49 I, Issue 5, 2002, Pages 2268-2273

  Desplanques, B ^a   Cornelis, J ^b   Achten, E ^c   Van De Walle, R ^a   Lemahieu, I ^a  

^a GHENT UNIVERSITY   (Belgium)

^b FREE UNIVERSITY OF BRUSSELS   (Belgium)

^c GHENT UNIVERSITY HOSPITAL   (Belgium)

Author keywords

Iterative image reconstruction; Magnetic resonance imaging (MRI); Pseudo inverse; System matrix

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; FAST FOURIER TRANSFORMS; IMAGE QUALITY; IMAGE RECONSTRUCTION; ITERATIVE METHODS; SIGNAL TO NOISE RATIO;

CARTESIAN GRID; SYSTEM MATRIX; VORONOI DIAGRAM;

MAGNETIC RESONANCE IMAGING;

EID: 0036815747     PISSN: 00189499     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNS.2002.803673     Document Type: Article

References (22)

1. A. F. Gmitro and A. L. Alexander, "Use of a projection reconstruction method to decrease motion sensitivity in diffusion-weighted MRI," Magn. Res. Med., vol. 29, pp. 835-838, 1993.
2. R. Van de Walle, I. Lemahieu, and E. Achten, "Two motion-detection algorithms for projection-reconstruction magnetic resonance imaging: Theory and experimental verification," Comput. Med. Imag. Graphics, vol. 22, no. 2, pp. 115-121, 1998.
3. C. B. Ahn, J. H. Kim, and Z. H. Cho, "High-speed spiral-scan echo planar NMR imaging," IEEE Trans. Med. Imag., vol. MI-5, pp. 2-7, 1986.
4. P. Börnert, H. Schomberg, B. Aldefeld, and J. Groen, "Improvements in spiral MR imaging," Magnetic Resonance Materials in Physics, Biology, and Medicine (MAGMA), vol. 9, pp. 29-41, 1999.
5. K. Scheffler and J. Hennig, "Frequency resolved single-shot MR imaging using stochastic k-space trajectories," Magn. Res. Med., vol. 35, pp. 569-576, 1996.
6. D. C. Noll, "Multi-shot Rosette trajectories for spectrally selective MR imaging," IEEE Trans. Med. Imag., vol. 16, pp. 372-377, 1997.
7. ____, "Simultaneous multislice acquisition using Rosette trajectories (SMART: A new imaging method for funcional MRI," Magn. Res. Med., vol. 39, pp. 709-716, 1998.
8. J. D. O'Sullivan, "A fast sinc function gridding algorithm for Fourier inversion in computer tomography," IEEE Trans. Med. Imag., vol. MI4, pp. 200-207, 1985.
9. J. I. Jackson, C. H. Meyer, D. G. Nishimura, and A. Macovski, "Selection of a convolution function for Fourier inversion using gridding," IEEE Trans. Med. Imag., vol. 10, pp. 472-478, 1991.
10. F. Wajer, R. Lethmate, J. A. C. Van Osch, D. Graveron-Demilly, M. Fuderer, and D. Van Ormondt, "Simple formula for the accuracy of gridding," in Proc. ISMRM, Glasgow, U.K., 2001, p. 776.
11. V. Rasche, R. Proksa, R. Sinkus, P. Bornert, and H. Eggers, "Resampling of data between arbitrary grids using convolution interpolation," IEEE Trans. Med. Imag., vol. 18, pp. 385-392, 1999.
12. J. G. Pipe and J. L. Duerk, "Analytical resolution and noise characteristics of linearly reconstructed magnetic resonance data with arbitrary k-space sampling," Magn. Res. Med., vol. 34, pp. 170-178, 1995.
13. M. F. Smith, "Generalized matrix inverse reconstruction for SPECT using a weighted singular value spectrum," IEEE Trans. Nucl. Sci., 43, pp. 2008-2017, 1996.
14. V. Selivanov and R. Lecomte, "Fast PET image reconstruction based on SVD decomposition of the system matrix," IEEE Trans. Nucl. Sci., 48, pp. 761-767, 2001.
15. R. Van de Walle, H. H. Barrett, K. J. Myers, M. I. Altbach, B. Desplanques, A. F. Gmitro, J. Cornelis, and I. Lemahieu, "Reconstruction of MR images from data acquired on a general nonregular grid by pseudoinverse calculation," IEEE Trans. Med. Imag., vol. 19, pp. 1160-1167, 2000.
16. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing. Cambridge, U.K.: Cambridge Univ. Press, 1997.
17. P. C. Hansel, "Rank deficient and discrete ill-posed problems," in Proc. SIAM, Philadelphia, PA, 1998.
18. A. Van der Sluis and H. A. van der Vorst, "The rate of convergence of conjugate gradients," Numer. Math, vol. 48, pp. 543-560, 1986.
19. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging. Piscataway, NJ: IEEE Press, 1987.
20. E. J. Hoffman, P. D. Cutler, W. M. Digby, and J. C. Mazziotta, "3-D phantom to simulate cerebral blood flow and metabolic images for PET," IEEE Trans. Nucl. Sci., vol. 37, pp. 616-620, 1990.
21. M. R. Hestenes and E. Stiefel, "Methods of conjugate gradients for solving linear systems," J. Res. Nat. Bur. Standards, vol. 49, pp. 409-436, 1952.
22. M. J. Firbank, A. Coulthard, R. M. Harrison, and E. D. Williams, "A comparison of two methods for measuring the signal to noise ratio on MR images," Phys. Med. Biol., vol. 44, pp. N261-N264, 1999.