Optical separable wavelet transform

De Cai; Qiaofeng Tan; Yingbai Yan; Guofan Jin; Qingsheng He

doi:10.1117/12.559614

4 November 2004 Optical separable wavelet transform

De Cai, Qiaofeng Tan, Yingbai Yan, Guofan Jin, Qingsheng He

Proceedings Volume 5556, Photonic Devices and Algorithms for Computing VI; (2004) https://doi.org/10.1117/12.559614
Event: Optical Science and Technology, the SPIE 49th Annual Meeting, 2004, Denver, Colorado, United States

Abstract

Although Optical wavelet transform has some advantages over discrete wavelet transform, but the mother wavelets to used are very few. That limits the signal processing ability of optical wavelet transform. Without scaling functions, the multiresolution analysis of a mother wavelet is not complete. In this paper, almost all the mother wavelets used in discrete wavelet transform are introduced into optical wavelet transform. Based on the analysis, we find whether the mother wavelets have analytical forms is not a necessary condition for implementing them in optical wavelet transform. Optical wavelet transform only needs to obtain the 2D approximations of wavelet functions. Then, with the cascade algorithm, the 1D approximations of scaling and wavelet functions are computed. By the scheme of 2D separable wavelet transform, the approximations of 2D scaling and wavelet functions are constructed. So mother wavelets frequently utilized in discrete wavelet transform are introduced into optical wavelet transform. With the increase of mother wavelet for selection, it is natural to classify optical wavelet transform into separable and non-separable cases as it does in discrete wavelet transform. Since the mothers introduced by the method in this paper are separable, they are included in the separable optical wavelet transform. And the advantages of the separable mothers are listed with corresponding examples.

Citation Download Citation

De Cai, Qiaofeng Tan, Yingbai Yan, Guofan Jin, and Qingsheng He "Optical separable wavelet transform", Proc. SPIE 5556, Photonic Devices and Algorithms for Computing VI, (4 November 2004); https://doi.org/10.1117/12.559614

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KEYWORDS

Wavelets

Discrete wavelet transforms

Wavelet transforms

Feature extraction

Optical filters

Signal processing

Fast wavelet transforms

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