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Efficient backward selection ofk-space samples in MRI on a hexagonal grid

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Abstract

Certain types of magnetic resonance imaging (MRI) such as magnetic resonance spectroscopic imaging and three-dimensional (3D) MRI require a great deal of time to acquire the image data. The acquisition time can be reduced if the image has a limited region of support, such as when imaging the brain or a cross section of the chest. Hexagonal sampling of the spatial frequency-domain (k-space) yields a 13.4% sampling density reduction compared to rectangular sampling of thek-space for images with a circular region of support (ROS) without incurring spatial aliasing in the reconstructed image. However, certain nonuniform sampling patterns are more efficient than hexagonal sampling for the same ROS. Sequential backward selection (SBS) has been used in previous work to optimize a nonuniform set ofk-space samples selected from a rectangular grid. To reduce the selection time, we present SBS of samples from a hexagonal grid. A Smith normal decomposition is used to transform the nonrectangular 2D discrete Fourier transform to a standard rectangular 2D fast Fourier transform so that the spatial-domain samples are represented directly on a rectangular grid without interpolation. The hexagonal grid allows the SBS algorithm to begin with a smaller set of candidate samples so that fewer samples have to be eliminated. Simulation results show that a significantly reduced selection time can be achieved with the proposed method in comparison with SBS on a rectangular grid.

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References

  1. K. F. Cheung, A Multidimensional Extension of Papoulis' Generalized Sampling Expansion with Applications in Minimum Density Sampling,Advanced Topics in Shannon Sampling and Interpolation Theory, Springer-Verlag, New York, pp. 85–119, 1993.

    Google Scholar 

  2. D. E. Dudgeon and R. M. Mersereau,Multidimensional Digital Signal Processing, Prentice-Hall, Englewood Cliffs NJ, 1984.

    Google Scholar 

  3. J. C. Ehrhardt, MR data acquisition and reconstruction using efficient sampling schemes,IEEE Trans. Medical Imaging, 9(3), 305–309, September 1990.

    Google Scholar 

  4. B. L. Evans, T. R. Gardos, and J. H. McClellan, Imposing structure on Smith-form decompositions of rational resampling matrices,IEEE Trans. Signal Process, 42(4), 970–973, April 1994.

    Google Scholar 

  5. Y. Gao and S. J. Reeves, Optimalk-space sampling in MRSI for images with a limited region of supprt, submitted.

  6. G. H. Golub and C. Van Loan,Matrix Computations, 2nd edition, Johns Hopkins University Press, Baltimore, MD, 1989.

    Google Scholar 

  7. A. Guessoum, Fast algorithms for the multidimensional discrete fourier transform, Ph.D. thesis, Georgia Institute of Technology, Atlanta GA, 1984.

    Google Scholar 

  8. A. Kaufmann and A. Henry-Labordère,Integer and Mixed Programming: Theory and Applications, Academic Press, New York, 1977.

    Google Scholar 

  9. T. F. Kirn, Magnetic resonance spectroscopy mày hold promise in studying metabolites, tissues,J. Am. Medical Assoc., 261, 1103ff, 1989.

    Google Scholar 

  10. R. M. Mersereau, The processing of hexagonally sampled two-dimensional signals,Proc. IEEE, 67, 930–949, 1979.

    Google Scholar 

  11. D. P. Petersen and D. Middleton, Sampling and reconstruction of wave-number limited functions inn-dimensional euclidean spaces,Inform. and Control, 5, 279–323, 1962.

    Google Scholar 

  12. W. H. Press et al.Numerical Recipes in C, Cambridge, Univ. Press, London, 1988.

    Google Scholar 

  13. S. J. Reeves, Selection ofk-space samples in localized spectroscopy of arbitrary volumes of interest,J. Magnet. Reson. Imaging, 5(2), 245–247, March/April 1995.

    Google Scholar 

  14. S. J. Reeves and L. P. Heck, Selection of observations in signal reconstruction,IEEE Trans. Signal Process., 43(3), 788–791, March 1995.

    Google Scholar 

  15. S. J. Reeves and Z. Zhao, New results on observation selection in signal reconstruction, inProceedings of the 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. III, pp. 1676–1679, 1996.

  16. S. J. Reeves and Z. Zhao, Sequential algorithms for observation selection,IEEE Trans. Signal Process., 47(1), 123–132, January 1999.

    Google Scholar 

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Authors and Affiliations

  1. Electrical and Computer Engineering Department, Auburn University, 36849, Auburn, Alabama, USA

    Yun Gao & Stanley J. Reeves

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  1. Yun Gao
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  2. Stanley J. Reeves
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This work was supported by a Biomedical Engineering Research Grant from the Whitaker Foundation.

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Gao, Y., Reeves, S.J. Efficient backward selection ofk-space samples in MRI on a hexagonal grid. Circuits Systems and Signal Process 19, 267–278 (2000). https://doi.org/10.1007/BF01200888

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  • DOI: https://doi.org/10.1007/BF01200888

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