Construction of periodic wavelet frames with dilation matrix |
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Authors: | Dayong Lu Dengfeng Li |
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Institution: | 1. Institute of Applied Mathematics, School of Mathematics and Information Sciences, Henan University, Kaifeng 475001, China; 2. School of Mathematics and Computer Science, Wuhan Textile University, Wuhan 430200, China |
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Abstract: | An important tool for the construction of periodic wavelet frame with the help of extension principles was presented in the Fourier domain by Zhang and Saito Appl. Comput. Harmon. Anal., 2008, 125: 68–186]. We extend their results to the dilation matrix cases in two aspects. We first show that the periodization of any wavelet frame constructed by the unitary extension principle formulated by Ron and Shen is still a periodic wavelet frame under weaker conditions than that given by Zhang and Saito, and then prove that the periodization of those generated by the mixed extension principle is also a periodic wavelet frame if the scaling functions have compact supports. |
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Keywords: | Periodic wavelet frames extension principle matrix dilation function periodization |
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