Multiwavelet Frames from Refinable Function Vectors |
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Authors: | Han Bin Mo Qun |
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Institution: | (1) Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada, T6G 2G1 |
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Abstract: | Starting from any two compactly supported d-refinable function vectors in (L
2(R))
r
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 d-wavelet frames in L
2(R) and they achieve the best possible orders of vanishing moments. When all the components of the two real-valued d-refinable function vectors are either symmetric or antisymmetric with their symmetry centers differing by half integers, such 2rd wavelet functions, which generate a pair of dual d-wavelet frames, can be real-valued and be either symmetric or antisymmetric with the same symmetry center. Wavelet frames from any d-refinable function vector are also considered. This paper generalizes the work in 5,12,13] 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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Keywords: | dual wavelet frames wavelet frames refinable function vectors multiwavelets refinable Hermite interpolants sum rules vanishing moments symmetry |
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