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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 31, Iss. 17 — Jun. 10, 1992
  • pp: 3267–3277

Wavelet transform as a bank of the matched filters

Harold Szu, Yunlong Sheng, and Jing Chen  »View Author Affiliations


Applied Optics, Vol. 31, Issue 17, pp. 3267-3277 (1992)
http://dx.doi.org/10.1364/AO.31.003267


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Abstract

The wavelet transform is a powerful tool for the analysis of short transient signals. We detail the advantages of the wavelet transform over the Fourier transform and the windowed Fourier transform and consider the wavelet as a bank of the VanderLugt matched filters. This methodology is particularly useful in those cases in which the shape of the mother wavelet is approximately known a priori. A two-dimensional optical correlator with a bank of the wavelet filters is implemented to yield the time–frequency joint representation of the wavelet transform of one-dimensional signals.

© 1992 Optical Society of America

History
Original Manuscript: August 20, 1991
Published: June 10, 1992

Citation
Harold Szu, Yunlong Sheng, and Jing Chen, "Wavelet transform as a bank of the matched filters," Appl. Opt. 31, 3267-3277 (1992)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-31-17-3267


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References

  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  2. J. M. Combes, A. Grossmann, Ph. Tchamitchian, eds. Wavelets, 2nd ed. (Springer-Verlag, Berlin, 1990). [CrossRef]
  3. H. Szu, “Matched filter spectrum shaping for light efficiency,” Appl. Opt. 24, 1426–1431 (1985). [CrossRef] [PubMed]
  4. H. Szu, J. Caufield, “The mutual time-frequency content of two signals,” Proc. IEEE 72, 902–908 (1984). [CrossRef]
  5. H. Szu, B. Telfer, A. Lohmann, “Modified wavelets that accommodate causality,” Opt. Eng. (to be published).
  6. E. Freysz, B. Pouligny, S. Argoul, A. Arneodo, “Optical wavelet transform of fractal aggregates,” Phys. Rev. Lett. 64, 745–748 (1990). [CrossRef] [PubMed]
  7. H. Szu, J.A. Blogett, “Self-reference spatiotemporal image restoration technique,” J. Opt. Soc. Am. 72, 1666–1669 (1982). [CrossRef]
  8. H. Szu, J. Caulfield, “Optical implementation of wavelet transform in high dimensions,” Appl. Opt. (to be published).
  9. A. Haar, “Zur Theorie der orthogonalen Funktionen-systeme,” Math. Annal. 69, 331–371 (1910). [CrossRef]
  10. Y. Meyer, “Principe d’incertitude, bases hibertiennes et algebres d’operation,” Semin. Boubaki 622 (1985).
  11. A. Grossmann, J. Morlet, “Decomposition of Hardy functions into square integrable wavelets of constant shape,” SIAM J. Math. Anal. 15, 723–736 (1984). [CrossRef]
  12. I. Daubechies, “The wavelet transform, time-frequency localization and signal analysis,” IEEE Trans. Inf. Theory 36, 961–1005 (1990). [CrossRef]
  13. S. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Machine Intell. 31, 674–693 (1989). [CrossRef]
  14. H. Szu, “Adaptive soliton wavelets,” Opt. Eng. (to be published).
  15. H. Szu, “Adaptive neural net wavelet theory,” Opt. Eng. (to be published).
  16. D. Gabor, “Theory of communication,” J. Inst. Electr. Eng. Part 3 93, 429–457 (1946).
  17. M. Bastiaans, “Gabor’s expansion of a signal into Gaussian elementary signals,” Proc. IEEE 68, 538–539 (1980). [CrossRef]
  18. J. Daugman, “Complete discrete 2-D Gabor transforms by neural networks for image analysis and compression,” IEEE Trans. Acoust. Speech and Signal Process. 36, 1169–1179 (1988). [CrossRef]
  19. Y. Zan, Y. Li, “Optical determination of Gabor coefficients of transient signals,” Opt. Lett. 16, 1031–1033 (1991). [CrossRef]
  20. K. H. Brenner, A. Lohmann, “Optical production of Wigner distributions,” Opt. Commun. 42, 310–314, (1982). [CrossRef]
  21. H. Szu, “Two dimensional optical processing of one-dimensional acoustic data,” Opt. Eng. 21, 804–813 (1982).
  22. H. Szu, “Application of Wigner and ambiguity functions to optics,” presented at the International Symposium on Circuits and Systems, San Jose, Calif., 5–7 May 1986.

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