The Gridding Method for Image Reconstruction by Fourier Transformation

IEEE Transactions on Medical Imaging

Volumn 14, Issue 3, 1995, Pages 596-607

  Schomberg, Hermann ^a   Timmer, Jan ^b  

^a PHILIPS RESEARCH LABORATORIES   (Germany)

^b PHILIPS HEALTHCARE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; COMPUTERIZED TOMOGRAPHY; ERRORS; FOURIER TRANSFORMS; IMAGE QUALITY; MAGNETIC RESONANCE IMAGING;

GRIDDING METHOD; RADON TRANSFORM; SMOOTHING EFFECT;

IMAGE RECONSTRUCTION;

EID: 0029378348     PISSN: 02780062     EISSN: 1558254X     Source Type: Journal    
DOI: 10.1109/42.414625     Document Type: Article

References (41)

1. D. B. Twieg, “The k-trajectory formulation of the NMR imaging process with applications in analysis and synthesis of imaging methods,” Med. Physics, vol. 10, no. 5, pp. 610–621, 1983.
2. D.C. Munson, J. D. O'Brien, and W. K. Jenkins, “A tomographic formulation of spotlight-mode synthetic aperture radar,” Proc. IEEE, vol. 71, no. 8, pp. 917–925, 1983.
3. W. N. Brouw, “Aperture synthesis,” in Methods in Computational Physics, B. Alder, S. Fernbach, and M. Rotenberg, Eds. New York: Academic, 1975, vol. 14, pp. 131–175.
4. G. T. Herman, Ed., Image Reconstruction from Projections: Implementation and Applications. Berlin: Springer-Verlag, 1979.
5. R. K. Mueller, M. Kaveh, and G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. IEEE, vol. 67, no. 4, pp. 567–587, 1979.
6. A. J. Devaney, “Inverse scattering theory foundations of tomography with diffracting wavefields,” in Int. Symp. Pattern Recognition Acoust. Imag., SPIE, vol. 786, pp. 2–6, 1987.
7. R. M. Mersereau, “Direct Fourier transform techniques in 3-D image reconstruction,” Comput. Biol. Med., vol. 6, pp. 247–258, 1976.
8. H. Stark, J. W. Woods, P. Indraneel, and P. Hingorani, “An investigation of computerized tomography by direct Fourier inversion and optimum interpolation,” IEEE Trans. Biomed. Eng., vol. BME-28, no. 7, pp. 496–505, 1981.
9. N. Niki, T. Mizutani, and Y. Takahashi, “A high-speed computerized tomography image reconstruction using direct two-dimensional Fourier transform method,” Syst.–Comput.–Contr., vol. 14, no. 3, pp. 56–65, 1983.
10. S. X. Pan and A. Kak, “A computational study of reconstruction algorithms for diffraction tomography: Interpolation versus filtered backprojection,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-31, no. 5, pp. 1262–1275. 1983.
11. R. M. Lewitt, “Reconstruction algorithms: Transform methods,” Proc. IEEE, vol. 71, no. 3, pp. 390–408, 1983.
12. F. Natterer, The Mathematics of Computerized Tomography. New York: Wiley, 1986.
13. H. Peng and H. Stark, “Direct Fourier reconstruction in fan-beam tomography,” IEEE Trans. Med. Imag., vol. MI-6, no. 3, pp. 209–219, 1987.
14. S. Matej and I. Bajla, “A high-speed reconstruction from projections using direct Fourier method with optimized parameters—An experimental analysis,” IEEE Trans. Med. Imag., vol. 9, no. 4, pp. 421–429, 1990.
15. A. R. Thompson and R. N. Bracewell, “Interpolation and Fourier transformation of fringe visibilities,” Astronomical J., vol. 79, no. 1, pp. 11–24, 1974.
16. J. D. O'Sullivan, “A fast sinc function gridding algorithm for Fourier inversion in computer tomography,” IEEE Trans. Med. Imag., vol. MI-4, no. 4, pp. 200–207, 1985.
17. C. H. Meyer, B. S. Hu, D. G. Nishimura, and A. Macovski, “Fast spiral coronary artery imaging,” Magn. Reson. Med., vol. 28, pp. 202–213, 1992.
18. M. Kaveh, M. Soumekh, and J. F. Greenleaf, “Signal processing for diffraction tomography,” IEEE Trans. Sonics Ultrason., vol. SU-31, pp. 230–238, 1984.
19. M. Kaveh and M. Soumekh, “Computer-assisted diffraction tomography,” in Image Recovery: Theory and Application, H. Stark, Ed. New York: Academic, 1987, pp. 369–413.
20. L. Schwartz, Théorie des Distributions, rev. ed. Paris: Hermann, 1966.
21. L. Hörmander, The Analysis of Linear Partial Differential Operators, 2nd ed. Berlin: Springer-Verlag, 1990.
22. A. Papoulis, Signal Analysis. New York: McGraw-Hill, 1977.
23. R. N. Bracewell, The Fourier Transform and its Applications, 2nd rev. ed. New York: McGraw-Hill, 1986.
24. J. W. Cooley, P. A. W. Lewis, and P. D. Welch, “Application of the fast Fourier transform to computation of Fourier integrals, Fourier series and convolution integrals,” IEEE Trans. Audio Electroacoust., vol. AU-15, no. 2, pp. 79–84, 1967.
25. E. O. Brigham, The Fast Fourier Transform. Englewood Cliffs, NJ: Prentice-Hall, 1974.
26. H. J. Nussbaumer, Fast Fourier Transform and Convolution Algorithms. Berlin: Springer-Verlag, 1981.
27. D. Slepian, “Some comments on Fourier analysis, uncertainty, and modeling,” SIAM Rev., vol. 25, no. 3, pp. 379–393, 1983.
28. F. R. Schwab, “Optimal gridding of visibility data in radio interferometry,” in Indirect Imaging, J. A. Roberts, Ed. New York: Cambridge Univ. Press, 1983, pp. 333–343.
29. 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, no. 3, pp. 473–478, 1991.
30. J. F. Kaiser, “Digital filters,” in System Analysis by Digital Computer, F. F. Kuo and J. F. Kaiser, Eds. New York: Wiley, 1966, pp. 218–285.
31. A. H. Nuttal, “Some windows with very good sidelobe behavior,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-29, no. 1, pp. 84–91, 1981.
32. S. W. Rowland, “Computer implementation of image reconstruction formulas,” in Image Reconstruction from Projections, G. T. Herman, Ed. Berlin: Springer-Verlag, 1979, pp. 9–79.
33. G. T. Herman, Image Reconstruction from Projections: The Fundamentals of Computerized Tomography. New York: Academic, 1980.
34. P. R. Edholm and G. T. Herman, “Linograms in image reconstruction from projections,” IEEE Trans. Med. Imag., vol. MI-6, no. 4, pp. 301–307, 1987.
35. P. Edholm, G. T. Herman, and D. A. Roberts, “Image reconstruction from linograms: Implementation and evaluation.” IEEE Trans. Med. Imag., vol. MI-7, no. 3, pp. 239–246. 1988.
36. H. Schomberg, “A transputer-based shuffle-shift machine for image processing and reconstruction,” in Proc. 10th Int. Conf. Pattern Recognition, IEEE Comput. Soc., 1990, pp. 445–450.
37. Transputer Databook, 2nd ed., Inmos, 1989.
38. T9000 Transputer Hardware Reference Manual, Inmos, 1993.
39. TMS320C4x User's Guide, Texas Instruments, 1991.
40. ADSP-21060 Preliminary User's Guide, Analog Devices, 1993.
41. J. Illingworth and J. Kittler, “A survey of the Hough transform,” Comput. Vision, Graphics, Image Processing, vol. 44, pp. 87–116, 1988.