Lifting scheme of biorthogonal wavelet transform based on discrete interpolatory splines

Amir Z. Averbuch; Alexander B. Pevnyi; Valery A. Zheludev

doi:10.1117/12.408645

4 December 2000 Lifting scheme of biorthogonal wavelet transform based on discrete interpolatory splines

Amir Z. Averbuch, Alexander B. Pevnyi, Valery A. Zheludev

Proceedings Volume 4119, Wavelet Applications in Signal and Image Processing VIII; (2000) https://doi.org/10.1117/12.408645
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

Abstract

In this paper, we present a new family of biorthogonal wavelet transforms and a related library of biorthogonal periodic symmetric waveforms. For the construction we used the interpolatory discrete splices which enabled us to design a library of perfect reconstruction filter banks. These filter banks are related to Buttersworth filters. The construction is performed in a 'lifting' manner. The difference from the conventional lifting scheme is that all the transforms are implemented in the frequency domain with the use of the fast Fourier transform. Two ways to choose the control filters are suggested. The proposed scheme is based on interpolation and, as such, it involves only samples of signals and it does not require any use of quadrature formulas. These filters have linear phase property and the basic waveforms are symmetric. In addition, these filters yield perfect frequency resolution.

Citation Download Citation

Amir Z. Averbuch, Alexander B. Pevnyi, and Valery A. Zheludev "Lifting scheme of biorthogonal wavelet transform based on discrete interpolatory splines", Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); https://doi.org/10.1117/12.408645

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