Frontiers of Mathematics in China >
Construction of periodic wavelet frames with dilation matrix
Received date: 20 Jul 2012
Accepted date: 24 Sep 2013
Published date: 01 Feb 2014
Copyright
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.
Dayong LU , Dengfeng LI . Construction of periodic wavelet frames with dilation matrix[J]. Frontiers of Mathematics in China, 2014 , 9(1) : 111 -134 . DOI: 10.1007/s11464-013-0335-5
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