A Performance Analysis of Fast Gabor Transform Methods

Graphical Models and Image Processing

Volumn 59, Issue 3, 1997, Pages 117-127

  Chinen, Troy T ^a   Reed, Todd R ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b University of California Davis   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; MATRIX ALGEBRA;

FAST GABOR TRANSFORMS; ZAK TRANSFORMS; ZAK-GABOR ALGORITHMS;

MATHEMATICAL TRANSFORMATIONS;

EID: 0031143666     PISSN: 10773169     EISSN: None     Source Type: Journal    
DOI: 10.1006/gmip.1997.0421     Document Type: Article

References (29)

1. Dennis Gabor, Theory of communication, J. Inst. Elec. Eng. (London) 93, 1946, 429-457.
2. Martin J. Bastiaans, Gabor's signal expansion and degrees of freedom of a signal, Opt. Acta, 29(9), 1982, 1223-1229.
3. Benjamin Friedlander and Boaz Porat, Detection of transient signals by the Gabor representation, Trans. Acoustics, Speech Signal Process. 37(2), 1989, 169-180.
4. Louis Auslander, Izidor C. Gertner, and Richard Tolimieri, The discrete transform application to time-frequency analysis and synthesis of nonstationary signals, IEEE Trans. Signal Process. 39(4), 1991, 825-835.
5. Roland Wilson and Goesta H. Granlund, The uncertainty principle in image processing, IEEE Trans. Pattern Anal. Mach. Intell. 6(6), 1984, 758-767.
6. John G. Daugman, Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters, J. Opt. Soc. Am. 2(7), 1985, 1160-1169.
7. John G. Daugman, Entropy reduction and decorrelation in visual coding by oriented neural receptive fields, IEEE Trans. Biomed. Eng. 36(1), 1989, 107-114.
8. Jezekiel Ben-Arie and K. Raghunath Rao, Nonorthogonal signal representation by Gaussians and Gabor functions, IEEE Trans. Circuits Systems, 42(6), 1995, 402-413.
9. John G. Daugman, Complete discrete 2-d Gabor transforms by neural networks for image analysis and compression, IEEE Trans. Acoustics, Speech, Signal Process. 36(7), 1988, 1169-1179.
10. Touradj Ebrahimi, Todd R. Reed, and Murat Kunt, Video coding using a pyramidal Gabor expansion, SPIE Vis. Commun. Image Process. 1360, 1990, 489-502.
11. Izidor C. Gertner and Yehoshua Y. Zeevi, Image representation with position-frequency localization, in Proceedings of IEEE ICASSP-91, Toronto, 1991. IEEE, pp. 2353-2356.
12. A. J. E. M. Janssen, Gabor representation of generalized functions, J. Math. Anal. Appl. 83, 1981, 377-394.
13. Ingrid Daubechies, Painless nonorthogonal expansions, J. Math. Phys. 27(5), 1986, 1271-1283.
14. 2(z) via frame theory, Signal Process. 40, 1994, 155-181.
15. Moshe Porat and Yehoshua Y. Zeevi, The generalized Gabor scheme of image representation in biological and machine vision, IEEE Trans. Pattern Anal. Mach. Intell. 10(4), 1988, 452-468.
16. Richard S. Orr, Derivation of the finite discrete Gabor transform by periodization and sampling, Signal Process. 34(1), 1993, 85-97.
17. Richard S. Orr, The order of computation for finite discrete Gabor transforms, IEEE Trans. Signal Process. 41(1), 1993, 122-130.
18. Liwa Wang, Chin-Tu Chen, and Wei-Chung Lin, An efficient algorithm to compute the complete set of discrete Gabor coefficients, IEEE Trans. Image Process. 3(1), 1994, 87-92.
19. Rogelio Balart, Matrix reformulation of the Gabor transform. SPIE Adaptive Signal Process. 1565, 1991, 447-457.
20. A. J. E. M. Janssen, The Zak transform: A signal transform for sampled time-continuous signals, Phillips J. Res. 43(1), 1988, 23-69.
21. Touradj Ebrahimi and Murat Kunt, Image compression by Gabor expansion, Opt. Eng. 30(7), 1991, 873-880.
22. J. Zak, Finite translations in solid physics, Phys. Rev. Lett. 19, 1967, 1385-1397.
23. Khaled Assaleh, Yehoshua Y. Zeevi, and Izidor C. Gertner, On the realization of the Zak-Gabor representation of images, SPIE Visual Commun. Image Process. 1606, 1991, 532-540.
24. M. An, M. Conner, and Richard Tolimieri, Computation and meaning of Gabor coefficients, SPIE Adaptive Signal Process. 1565, 1991, 383-401.
25. Richard Tolimieri and M. Conner, Zak transform as an adaptive tool, SPIE Adaptive Signal Process. 1565, 1991, 345-356.
26. Einar Hille, Analytic Function Theory, Ginn, Needham Heights, MA, 1959.
27. Hong Yan and John C. Gore, Weight adjustment rule of neural networks for computing discrete 2-d Gabor transforms, IEEE Trans. Acoustics, Speech, Signal Process. 38(9), 1990, 1654-1656.
28. V. Srinivasan, P. Bhatia, and S. H. Ong, A fast implementation of the discrete 2-d Gabor transform, Signal Process. 31(2), 1993, 229-233.
29. William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery, Numerical Recipes in C: The Art of Scientific Computing. Cambridge Univ. Press, Cambridge, UK, 1992.