Analysis of the direct Fourier method for computer tomography

IEEE Transactions on Medical Imaging

Volumn 19, Issue 3, 2000, Pages 211-222

  Waiden, Johan ^a  

^a YALE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; FOURIER TRANSFORMS; FUNCTIONS; IMAGE RECONSTRUCTION; INTERPOLATION; SAMPLING; X RAY APPARATUS;

DIRECT FOURIER METHOD; RADON TRANSFORM;

COMPUTERIZED TOMOGRAPHY;

ALGORITHM; ARTICLE; COMPARATIVE STUDY; COMPUTER ASSISTED TOMOGRAPHY; FOURIER ANALYSIS; HUMAN; IMAGE QUALITY; REPRODUCIBILITY; STANDARD;

ALGORITHMS; FOURIER ANALYSIS; HUMANS; PHANTOMS, IMAGING; REPRODUCIBILITY OF RESULTS; TOMOGRAPHY, X-RAY COMPUTED;

EID: 0033623973     PISSN: 02780062     EISSN: None     Source Type: Journal    
DOI: 10.1109/42.845179     Document Type: Article

References (18)

1. R. M. Lewitt, "Reconstruction algorithms: Transform methods," Proc. IEEE, vol. 71, no. 3, pp. 39008, 1982.
2. F. Natterer, The Mathematics of Computerized Tomography. New York: Wiley, 1986.
3. H. Stark, J. W. Woods, I. Paul, and R. Hingorani, "An investigation of computerized tomography by direct Fourier inversion and optimum interpolation," IEEE Trans. Biomed. Eng., vol. 28, pp. 496-505, 1981.
4. A. Brandt, "An O(N2 log N) multilevel backprojection method,"The Weizmann Institute of Science, Tech. Rep. WI/GC-6, 1997.
5. S. Nilsson, "Application of fast backprojecton techniques for some inverse problems of integral geometry," Ph.D. dissertation, Linköping Univ., Linköping, Sweden, 1997.
6. P. Edholm and G. T Herman, "Linograms in image reconstruction from projections," IEEE Trans. Med. Imag., vol. MI-6, pp. 301-307, 1987.
7. P. Edholm, G. T Herman, and D. A. Roberts, "Image reconstruction from linograms: Implementation and evaluation," IEEE Trans. Med. Imag., vol. 7, pp. 239-246, 1988.
8. D. Gottlieb and B. Gustafsson, "On the direct Fourier method for computer tomography," Dept. of Scientific Computing, Uppsala Univ., Tech. Rep. 207, 1998.
9. M. Magnusson, "Linogram and other direct Fourier methods for tomographic reconstruction," Ph.D. dissertation, Dept. of Electrical Engineering, Linköping Univ., Linköping, Sweden, 1993.
10. J. D. O'Sullivan, "A fast sine function gridding algorithm for Fourier inversion in computer tomography," IEEE Trans. Med. Imag., vol. MI-4, pp. 200-207, 1985.
11. H. Schomberg and J. Timmer, "The gridding method for image reconstruction by Fourier transformation," IEEE Trans. Med. Imag., vol. 14, pp. 595-607, 1995.
12. G. Beylkin, "On the fast Fourier transform of functions with singularities," Appl. Comput. Harmon. Anal., vol. 2, no. 4, pp. 363-381, 1995.
13. B. Gustafsson, "Mathematics for computer tomography," Physica Scripta, vol. T61, pp. 38-13, 1996.
14. J. Waiden, "On the approximation of singular source terms in differential equations," Numerical Methods Partial Differential Equations, vol. 15, no. 4, pp. 503-520, 1999.
15. [ 15] N. I. Akhiezer, The Calculus of Variations. New York: Blaisdell, 1962.
16. [ 16] C. K. Chui, An Introduction to Wavelets. New York: Academic, 1992.
17. L. A. Shepp and B. F. Logan, "The Fourier reconstruction of a head section," IEEE Trans. Nucl. Sei., vol. 21, pp. 21-13, 1974.
18. L. Hörmander, The Analysis of Linear Partial Differential Operator I. Berlin, Germany: Springer Verlag, 1990.