Local analysis,cardinality, and split trick of quasi-biorthogonal frame wavelets |
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Authors: | Zhi Hua Zhang |
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Affiliation: | College of Global Change and Earth System Science, Beijing Normal University, Beijing 100875, P. R. China |
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Abstract: | The notion of quasi-biorthogonal frame wavelets is a generalization of the notion of orthogonal wavelets. A quasi-biorthogonal frame wavelet with the cardinality r consists of r pairs of functions. In this paper we first analyze the local property of the quasi-biorthogonal frame wavelet and show that its each pair of functions generates reconstruction formulas of the corresponding subspaces. Next we show that the lower bound of its cardinalities depends on a pair of dual frame multiresolution analyses deriving it. Finally, we present a split trick and show that any quasi-biorthogonal frame wavelet can be split into a new quasi-biorthogonal frame wavelet with an arbitrarily large cardinality. For generality, we work in the setting of matrix dilations. |
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Keywords: | Local analysis cardinality split trick quasi-biorthogonal frame wavelets |
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