A dual-chain approach for bottom-up construction of wavelet filters with any integer dilation

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• 作者：Charles K. Chui^a ; ¹ ; ^{ckchui@stanford.edu} ; Bin Han^b ; ² ; ^{bhan@ualberta.ca} ; Xiaosheng Zhuang^c ; ² ; ^{xzhuang@math.tu-berlin.de}
• 关键词：Dual-chain method ; Biorthogonal wavelets ; Bottom&ndash ; up wavelet filter construction ; Lazy wavelets ; Symmetry property ; Integer dilation ; Polyphase matrices ; CBC algorithm
• 刊名：Applied and Computational Harmonic Analysis
• 出版年：2012
• 期刊代码：119_10635203
• 类别：cp
• 出版时间：September, 2012
• 卷：33
• 期：2
• 页码：204-225
• 文件大小：820 K

摘要

A dual-chain approach is introduced in this paper to construct dual wavelet filter systems with an arbitrary integer dilation . Starting from a pair of -dual low-pass filters, with , a top-down chain of filters is constructed with consecutive -dual pairs , , and , where and for all , and denotes the number of filter taps of . This enables the formulation of the filter system , with , to be used as the second component of the initial filter system of the bottom-up -dual chain: , constructed bottom-up iteratively, from to , by using both the -duality property of , and the unimodular property of the polyphase Laurent polynomial matrix associated with the filter system . Then the desired dual wavelet filter systems, associated with a and , are given by and . More importantly, the constructive algorithm for this dual-chain approach can be appropriately modified to preserve the symmetry property of the initial -dual pair . For any dilation factor , the dual-chain algorithms developed in this paper provide two systematic methods for the construction of both biorthogonal wavelets and bottom-up wavelets with or without the symmetry property.