Library of biorthogonal wavelet transforms originated from polynomial splines

Amir Z. Averbuch; Valery A. Zheludev

doi:10.1117/12.449718

5 December 2001 Library of biorthogonal wavelet transforms originated from polynomial splines

Amir Z. Averbuch, Valery A. Zheludev

Proceedings Volume 4478, Wavelets: Applications in Signal and Image Processing IX; (2001) https://doi.org/10.1117/12.449718
Event: International Symposium on Optical Science and Technology, 2001, San Diego, CA, United States

Abstract

We present a library of biorthogonal wavelet transforms and the related library of biorthogonal symmetric waveforms. For the construction we use interpolatory, quasiinterpolatory and smoothing splines with finite masks (local splines). With this base we designed a set of perfect reconstruction infinite and finite impulse response filter banks with linear phase property. The construction is performed in a lifting manner. The developed technique allows to construct wavelet transforms with arbitrary prescribed properties such as the number of vanishing moments, shape of wavelets, and frequency resolution. Moreover, the transforms contain some scalar control parameters which enable their flexible tuning in either time or frequency domains. The transforms are implemented in a fast way. The transforms, which are based on interpolatory splines, are implemented through recursive filtering. We present encouraging results towards image compression.

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Amir Z. Averbuch and Valery A. Zheludev "Library of biorthogonal wavelet transforms originated from polynomial splines", Proc. SPIE 4478, Wavelets: Applications in Signal and Image Processing IX, (5 December 2001); https://doi.org/10.1117/12.449718

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