Two-dimensional wavelet transform achieved by computer-generated multireference matched filter and Dammann grating.

A two-dimensional wavelet transform is optically performed in real time by use of a new multichannel system that processes the different daughter wavelets separately. The system, which is able to handle every wavelet function, relies on a Dammann grating for generating a multichannel array. All channels are processed in parallel by a conventional two-dimensional correlator. Experimental results applying Morlet-wavelet decomposition are presented.

[1]  M. E. Prise,et al.  Dammann Gratings For Laser Beam Shaping , 1989 .

[2]  Y Li,et al.  Optical realization of wavelet transform for a one-dimensional signal. , 1992, Optics letters.

[3]  Harold H. Szu,et al.  Parallel discrete and continuous wavelet transforms , 1992 .

[4]  Dennis Gabor,et al.  Theory of communication , 1946 .

[5]  Yehoshua Y. Zeevi,et al.  The Generalized Gabor Scheme of Image Representation in Biological and Machine Vision , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  Danny Roberge,et al.  Optical wavelet transform , 1992 .

[7]  Richard Kronland-Martinet,et al.  Analysis of Sound Patterns through Wavelet transforms , 1987, Int. J. Pattern Recognit. Artif. Intell..

[8]  Argoul,et al.  Optical wavelet transform of fractal aggregates. , 1990, Physical review letters.

[9]  H. Dammann,et al.  High-efficiency in-line multiple imaging by means of multiple phase holograms , 1971 .

[10]  Erhard Klotz,et al.  Coherent Optical Generation and Inspection of Two-dimensional Periodic Structures , 1977 .

[11]  A. Grossmann,et al.  DECOMPOSITION OF HARDY FUNCTIONS INTO SQUARE INTEGRABLE WAVELETS OF CONSTANT SHAPE , 1984 .

[12]  D Mendlovic,et al.  Optical realization of the wavelet transform for two-dimensional objects. , 1993, Applied optics.

[13]  M.O. Freeman,et al.  Multi-scale optical image processing , 1991, 1991., IEEE International Sympoisum on Circuits and Systems.

[14]  Ingrid Daubechies,et al.  The wavelet transform, time-frequency localization and signal analysis , 1990, IEEE Trans. Inf. Theory.

[15]  D X Wang,et al.  Two-dimensional optical wavelet transform in space domain and its performance analysis. , 1994, Applied optics.

[16]  M. Bastiaans,et al.  Gabor's expansion of a signal into Gaussian elementary signals , 1980, Proceedings of the IEEE.

[17]  Danny Roberge,et al.  Optical N4 implementation of a two-dimensional wavelet transform , 1992 .

[18]  H. Szu.  Matched filter spectrum shaping for light efficiency. , 1985, Applied optics.

[19]  Ph. Tchamitchian,et al.  Wavelets: Time-Frequency Methods and Phase Space , 1992 .

[20]  H.H. Szu,et al.  The mutual time—Frequency content of two signals , 1984, Proceedings of the IEEE.

[21]  Y Sheng,et al.  Wavelet transform as a bank of the matched filters. , 1992, Applied optics.