Resampling of data between arbitrary grids using convolution interpolation

IEEE Transactions on Medical Imaging

Volumn 18, Issue 5, 1999, Pages 385-392

  Rasche, V ^a   Proksa, R ^a   Sinkus, R ^a   Bornert P ^a   Eggers, H ^a  

^a PHILIPS RESEARCH LABORATORIES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONVOLUTION; DATA REDUCTION; IMAGE ANALYSIS; IMAGE RECONSTRUCTION; INTERPOLATION; PROBABILITY DENSITY FUNCTION;

ARBITRARY GRIDS; CONVOLUTION INTERPOLATION; VORONOI DIAGRAM;

MEDICAL IMAGING;

ALGORITHM; ARTICLE; COMPUTER ASSISTED TOMOGRAPHY; COMPUTER PROGRAM; FOURIER ANALYSIS; HUMAN; IMAGE QUALITY; NUCLEAR MAGNETIC RESONANCE IMAGING; STATISTICAL ANALYSIS; STATISTICS;

ALGORITHMS; DATA INTERPRETATION, STATISTICAL; FOURIER ANALYSIS; HUMANS; MAGNETIC RESONANCE IMAGING; PHANTOMS, IMAGING; SOFTWARE; TOMOGRAPHY, X-RAY COMPUTED;

EID: 0032588591     PISSN: 02780062     EISSN: None     Source Type: Journal    
DOI: 10.1109/42.774166     Document Type: Article

References (29)

1. J. J. Clark, M. R. Palmer, and P. D. Lawrence, "A transformation method for the reconstruction of functions from nonuniformly spaced samples," IEEE Trans. Acoust, Speech, Signal Processing, vol. ASSP-33, no. 4, pp. 1151-1164, 1985.
2. J. O'Sulllivan, "A fast sine function gridding algorithm for Fourier inversion in computed tomography," IEEE Trans. Med. Imag., vol. MI-4, no. 4, pp. 200-207, 1985.
3. W. N. Brouw, "Aperture synthesis," in Methods in Computational Physics, B. Alder, S. Fernbach, and M. Rotenberg Eds. New York: Academic, 1986, vol. 14, pp. 131-175. [4] A. Takahashi and T. M. Peters, "Measurement of fc-space trajectories for rf-pulse design," in Proc 12th Meeting SMRM, 1993, p. 424.
4. D. M. Spielman and J. M. Pauly, "Spiral imaging on a small-bore system at 4.7 t," Magn. Reson. Med., vol. 34, pp. 580-585, 1995.
5. K. F. King, T. K. F. Foo, and C. R. Crawford, "Optimized gradient waveforms for spiral imaging," Magn. Reson. Med., vol. 34, pp. 156-160, 1995.
6. J. R. Liao, J. M. Pauly, and N. J. Pelc, "MR imaging using piecewiselinear spiral trajectories," in Proc. 4th Meeting ISMRM, 1996, p. 390.
7. J. R. Liao and N. J. Pelc, "Image reconstruction of generalized spiral trajectories," in Proc. 4th Meeting ISMRM, 1996, p. 359.
8. C. H. Meyer, B. S. Hu, D. G. Nishimura, and A. Mcovski, "Fast spiral coronary artery imaging," Magn. Reson. Med., vol. 28, pp. 202-213, 1992.
9. D. C. Noll, J. A. Webb, and T. E. Warfel, "Parallel data resampling and Fourier inversion by the scane-line method," IEEE Trans. Med. Imag., vol. 14, no. 3, pp. 454-463, 1995.
10. P. Irarrazabal and D. G. Nishimura, "Fast three dimensional magnetic resonance imaging," Magn. Reson. Med., vol. 33, pp. 656-662, 1995.
11. R. D. Hoge, R. K. S. Kwan, and G. B. Pike, "Density compensation functions for spiral MRI," Magn. Reson. Med., vol. 38, pp. 117-128, 1997.
12. M. G. Voronoi, "Nouvelles applications des parameters continus a la théorie des formes quardratiques," J. Reine Angew. Math., vol. 134, pp. 198-287, 1908.
13. F. Aurenhammer, "Voronoi diagrams-A survey of a fundamental data structure," ACM Comput. Surveys, vol. 23, pp. 345-4105, 1991.
14. L. Lemieux, R. Jagoe, D. R. Fish, N. D. Kitchen, and D. G. T. Thomas, "A patient-to-computed-tomography image registration method based on digitally reconstructed radiographs," J. Med. Phys., vol. 9, no. 3, pp. 245-261, 1990.
15. J. Weese, T. M. Buzug, C. Lorenz, and C. Fassnacht, "An approach to 2dβd registration of a vertebra in ct with its profile in x-ray projections," in CVRMed-MRCAS'97, Lecture Notes in Computer Science 1205. Berlin, Germany: Springer-Verlag, 1997, pp. 119-128.
16. G. T. Herman, Image Reconstruction from Projections: The Fundamentals of Computerized Tomography Orlando, FL: Academic, 1980.
17. G. D'Agostini, "A multidimensional unfolding method based on Bayes' theorem," Nucl. Instrum. Meth. Phys. Res., vol. A 362, pp. 487-4198, 1995.
18. M. Levoy, "Efficient ray tracing of volume data," ACM Trans. Graph., vol. 21, pp. 1749-1760, 1994.
19. S. Napel, S. Dünne, and B. Rutt, "Fast Fourier projection for MR angiography," Magn. Reson. Med., vol. 19, pp. 393-4105, 1991.
20. V. Rasche, T. Köhler, and R. Proksa, "Iterative reconstruction of MR data sampled along spiral trajectories using convolution-interpolation without knowledge of the density compensation function," in Proc. 15th Meeting, ESMRMB, Geneva, Switzerland, 1998, p. 352.
21. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. New York: McGraw-Hill, 1986.
22. R. M. Lewitt, "Reconstruction algorithms: Transform methods," in Proc. IEEE, vol. 71, pp. 390-408, 1983.
23. A. R. Thompson and R. N. Bracewell, "Interpolation and Fourier transformation of fringe visibilities," Astronom. J., vol. 79, pp. 11-24, 1973.
24. M. L. Lauzon and B. K. Rutt, "Effects of polar sampling in fc-space," Magn. Reson. Med., vol. 36, pp. 940-949, 1996.
25. 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. MI-10, no. 3, pp. 473-478, 1985.
26. H. Schomberg and J. Timmer, "The gridding method for image reconstruction by Fourier transformation," IEEE Trans. Med. Imag., vol. 14, no. 3, pp. 596-607, 1995.
27. B. N. Delaunay, "Sur la sphere vide," Bull. Acad. Sci. USSR VII: Class. Sci. Math., pp. 793-800, 1934.
28. J. A. den Boer and M. T. Vlaardingerbroek, Magnetic Resonance Imaging. Berlin, Germany: Springer-Verlag, 1996.
29. G. F. Mason, T. Harshberger, H. Herington, Y. Zhang, G. Prohost, and D. B. Twieg, "A method to measure arbitrary fc-space trajectories in rapid MR imaging," Magn. Reson. Med., vol. 38, p. 492, 1997.