Non-Equispaced Fast Fourier Transforms with Applications to Tomography

Journal of Fourier Analysis and Applications

Volumn 9, Issue 5, 2003, Pages 431-450

  Fourmont, Karsten ^a  

^a UNIVERSITY OF MÜNSTER   (Germany)

Author keywords

Computerized tomography; Fast Fourier Transform; Fourier analysis; Fourier reconstruction algorithms; Interpolation; Radon transform

Indexed keywords

EID: 0742289178     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00041-003-0021-1     Document Type: Article

References (18)

1. Averbuch, A., Coifman, R., Donoho, D., Israeli, M., and Waldén, J. (2000). The Pseudopolar FFT and its Applications, Technical Report, School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
2. Beylkin, G. (1995). On the fast Fourier transform of functions with singularities, Appl. Camp. Harm. Anal., 2, 363-381.
3. Brouw, W.N. (1975). Aperture synthesis, in Methods in Computational Physics, Alder, B., Fernbach, S., and Rotenberg, M., Eds., 14, 131-175.
4. Dutt, A. and Rokhlin, V. (1993). Fast Fourier transforms for nonequispaced data, SIAM J. Sci. Comput., 14, 1368-1393.
5. Kaiser, J.F. (1966), Digital filters, in System Analysis by Digital Computers, Kuo, F. and Kaiser, J.F., Eds., 218-285.
6. Kaveh, M. and Soumekh, M. (1987). Computer-assisted diffraction tomography, in Image Recovery: Theory and Application, Stark, H., Ed., 369-413.
7. Natterer, F. (1985). Fourier reconstruction in tomography, Numerische Mathematik, 47, 343-353.
8. Natterer, F. (1986). The Mathematics of Computerized Tomography, John Wiley & Sons and B.G. Teubner.
9. O'Sullivan, J.D. (1985). A fast sinc function gridding algorithm for Fourier inversion in computer tomography, IEEE Trans Med. Imag., MI-4(4), 200-207.
10. Schomberg, H. and Timmer, J. (1995). The gridding method for image reconstruction by Fourier transformation, IEEE Trans. Med. Imag., 14(3), 596-607.
11. Slepian, D. (1983). Some comments on Fourier analysis, uncertainty, and modeling, SIAM Rev., 25, 379-393.
12. Steidl, G. (1998). A note on fast Fourier transforms for nonequispaced grids, Advances in Computational Mathematics, 9, 337-352.
13. Twieg, D.B. (1983). The k-trajectory formulation of the NMR imaging process with applications in analysis and synthesis of imaging methods, Med. Physics, 10(5), 610-621.
14. Ware, A. (1998). Fast approximate Fourier transforms for irregularly spaced data, SIAM Review, 40, 838-856.
15. Fourmont, K. (1999). Schnelle Fourier - Transformation bei nichtäquidistanten Gittern und tomographische Anwendungen, Dissertation, University of Münster.
16. Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. (1988). Numericla Recipes, Cambridge University Press.
17. Stoer, J. and Bulirsch, R. (1980). Introduction to Numerical Analysis, Springer-Verlag.
18. Potts, D. and Steidl, G. (2002). Fourier reconstruction of functions from their nonstandard sampled Radon transform, J. Fourier Anal. Appl., 8(6), 513-533.