Optical wavelet packet transform and best basis selecting by a volume holographic opto-electronic hybrid system

Wavelet packet transform analyzes signals more finely than wavelet transform does. This advantage can be utilized in optical wavelet transform. To introduce wavelet packet transform into optics, mother wavelets that have scaling functions must be used. If the scaling function does not have analytical formula, its approximation can be computed using the cascade algorithm. With the refinement relationship, its wavelet function can by calculated. After the 1-D wavelet packet bases are obtained, 2-D separable wavelet packet bases can be constructed for optical wavelet packet transform. As an example, a volume holographic opto-electronic system is proposed to fulfill joint best basis selection for a face image bank with the mother Db3.

[1]  Paulo Acioly M. dos Santos,et al.  Photorefractive optical holographic correlation using a Bi12TiO20 crystal at λ=0.633 μm , 1991 .

[2]  Francis T. S. Yu,et al.  Wavelength multiplexed reflection matched spatial filters using LiNbO3 , 1991 .

[3]  W Wang,et al.  Joint wavelet-transform correlator for image feature extraction. , 1995, Applied optics.

[4]  R. Coifman,et al.  Entropy-based Algorithms for Best Basis Selection from Which We Can Estimate a L+1 2 2 L . Thus a Signal of N = 2 L Points Can Be Expanded in 2 N Diierent , 1992 .

[5]  Deepen Sinha,et al.  On the optimal choice of a wavelet for signal representation , 1992, IEEE Trans. Inf. Theory.

[6]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Yingbai Yan,et al.  Multiplexing of volume holographic wavelet correlation processor , 2000 .

[8]  Mladen Victor Wickerhauser.  Fast approximate factor analysis , 1992, Other Conferences.

[9]  Yingbai Yan,et al.  Invariant performance of a volume holographic wavelet correlation processor , 2000 .

[10]  Y Sheng,et al.  Continuous-scale-invariant pattern recognition with adaptive-wavelet-matched filters. , 1999, Applied optics.

[11]  Yingbai Yan,et al.  Volume holographic wavelet correlation processor , 2000 .

[12]  Yingbai Yan,et al.  Wavelet transform to improve recognition accuracy of a volume holographic correlator , 1999, Other Conferences.

[13]  Ronald A. DeVore,et al.  Image compression through wavelet transform coding , 1992, IEEE Trans. Inf. Theory.

[14]  I. Daubechies.  Ten Lectures on Wavelets , 1992 .

[15]  David Casasent,et al.  Optical correlation filter fusion for object detection , 1994 .

[16]  John G. Daugman,et al.  Complete discrete 2-D Gabor transforms by neural networks for image analysis and compression , 1988, IEEE Trans. Acoust. Speech Signal Process..

[17]  Harold H. Szu,et al.  Neural network adaptive wavelets for signal representation and classification , 1992 .

[18]  Yingbai Yan,et al.  Image feature extraction with the optical Haar wavelet transform , 1995 .

[19]  Yingbai Yan,et al.  Multichannel wavelet correlators by the use of associative storage in a photorefractive material , 1998, Other Conferences.

[20]  Francis T. S. Yu,et al.  Wavelet matched filtering using a photorefractive crystal , 1993 .

[21]  Francis T. S. Yu,et al.  Bragg diffraction-limited photorefractive crystal-based correlators , 1995 .

[22]  Truong Q. Nguyen,et al.  Wavelets and filter banks , 1996 .