Fast Implementation of the Continuous Wavelet Transform with Integer Scales

IEEE Transactions on Signal Processing

Volumn 42, Issue 12, 1994, Pages 3519-3523

  Unser, Michael ^a   Aldroubi, Akram ^a   Schiff, Steven J ^b  

^a NATIONAL INSTITUTES OF HEALTH   (United States)

^b CHILDREN'S NATIONAL MEDICAL CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; DIGITAL FILTERS; MATHEMATICAL MODELS; POLYNOMIALS; WAVELET TRANSFORMS;

FAST NONITERATIVE ALGORITHM; SPLINE WAVELETS;

SIGNAL DETECTION;

EID: 0028714160     PISSN: 1053587X     EISSN: 19410476     Source Type: Journal    
DOI: 10.1109/78.340787     Document Type: Article

References (21)

1. I. Daubechies, Ten Lectures on Wavelets. Philadelphia: Soc. Indus. Applied Math., 1992.
2. A. Grossmann and J. Morlet, “Decomposition of Hardy functions into square integrable wavelets of constant shape,” SIAM J. Math. Anal., vol. 15, no. 4, pp. 723-736, July 1984.
3. O. Rioul and M. Vetterli, “Wavelets and signal processing,” IEEE Signal Processing Mag., vol. 8, no. 4, pp. 11-38, Oct. 1991.
4. S. G. Mallat, “A theory of multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Patt. Anal. Machine Intell., vol. 11, no. 7, pp. 674-693, 1989.
5. M. J. Shensa, “The discrete wavelet transform: wedding the a trous and Mallat algorithms,” IEEE Trans. Signal Processing, vol. 40, no. 10, pp. 2464-2482, Oct. 1992.
6. O. Rioul and P. Duhamel, “Fast algorithms for discrete and continuous wavelet transforms,” IEEE Trans Inform. Theory, vol. 38, no. 2, pp. 569-586, Mar. 1992.
7. M. Unser and A. Aldroubi, “Polynomial splines and wavelets A signal processing perspective,” in Wavelets A Tutorial in Theory and Applications (C. K. Chui, Ed.). San Diego: Academic, 1992, pp. 91-122.
8. I. J. Schoenberg, “Contribution to the problem of approximation of equidistant data by analytic functions,” Quart. Appl. Math., vol. 4, pp. 45-99, 112-141, 1946.
9. M. Unser, A. Aldroubi, and M. Eden, “ B-spline signal processing. Part I: Theory,” IEEE Trans. Signal Processing, vol. 41, no. 2, pp. 821-833, Feb. 1993.
10. “Fast B-spline transforms for continuous image representation and interpolation,” IEEE Trans. Patt. Anal. Machine Intell., vol. 13, no. 3, pp. 277-285, Mar. 1991.
11. “Polynomial spline signal approximations: Filter design and asymptotic equivalence with Shannon's sampling theorem,” IEEE Trans. Inform. Theory, vol. 38, no. 1, pp. 95-103, Jan. 1992.
12. S. Mallat and W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inform. Theory, vol. 38, no. 2, pp. 617-643, Mar. 1992.
13. J. F. Canny, “A computational approach to edge detection,” IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-8, no. 6, pp. 679-697, 1986.
14. D. Marr and E. Hildreth, “Theory of edge detection,” Proc. Roy. Soc. London, vol. B 207, pp. 187-217, 1980.
15. M. Unser, A. Aldroubi, and M. Eden, “On the asymptotic convergence of B-spline wavelets to Gabor functions,” IEEE Trans. Inform. Theory, vol. 38, no. 2, pp. 864-872, Mar. 1992.
16. C. K. Chui and J. Z. Wang, “On compactly supported spline wavelets and a duality principle,” Trans. Amer. Math. Soc., vol. 330, no. 2, pp. 903-915, 1992.
17. M. Unser, A. Aldroubi, and M. Eden, “A family of polynomial spline wavelet transforms,” Signal Processing, vol. 30, no. 2, pp. 141-162, Jan. 1993.
18. D. L. Jones and R. G. Baraniuk, “Efficient approximation of continuous wavelet transforms,” Electron. Lett, vol. 27, no. 9, pp. 748-750, Apr. 1991.
19. S. Schiff, A. Aldroubi, M. Unser, and S. Sato, “Fast wavelet transform of EEG,” Electroencephalog. Clin. Neurophysiol., in press.
20. S. J. Schiff, J. Heller, S. L. Weinstein, and J. Milton, “Wavelet transforms and surrogate data for electroencephalographic spike and seizure detection,” Opt. Eng., vol. 33, pp. 2162-2169, 1994.
21. A. Aldroubi, M. Unser, and M. Eden, “Cardinal spline filters: Stability and convergence to the ideal sine interpolator,” Signal Processing, vol. 28, no. 2, pp. 127-138, Aug. 1992.