Multiwavelet Frames From Refinable Function Vectors

Bin Han and Qun Mo


Starting from any two compactly supported $d$-refinable function vectors with multiplicity $r$ and dilation factor $d$, we show that it is always possible to construct $2rd$ wavelet functions with compact support such that they generate a pair of dual wavelet frames in $L_2(\RR)$. The constructed wavelet functions achieve the best possible orders of vanishing moments and are real-valued symmetric functions provided that the two refinable function vectors are real-valued and symmetric. Wavelet frames from any refinable function vector are also considered. This paper generalizes the work in \cite{CHS, DHRS, DH} on constructing dual wavelet frames from scalar refinable functions to the multiwavelet case. Examples are provided to illustrate the construction in this paper.

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