Abstract
In multi-wavelet decomposition techniques for the analysis of a given vector-valued signal, it is desirable with respect to the computational efficiency of the associated algorithms that the low-pass and high-pass matrix filters sequences be as short as possible. By applying a multi-wavelet construction method based on the solving of a system of four matrix Laurent polynomial identities, and using as main building block a class of arbitrarily smooth refinable vector splines, we establish an explicitly formulated class of shortest possible associated matrix filter sequences for decomposition, as well as minimally supported spline multi-wavelets for these optimal filter sequences.
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The authors would like to express their sincere gratitude to the reviewers, whose several helpful suggestions and comments contributed to the improvement of this paper.
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The authors would like to thank the African Institute for Mathematical Sciences (AIMS) in South Africa for its support.
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Communicated by: Tomas Sauer
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de Villiers, J., Ranirina, D. Shortest multi-wavelet matrix filters for refinable vector splines. Adv Comput Math 45, 3327–3365 (2019). https://doi.org/10.1007/s10444-019-09740-7
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DOI: https://doi.org/10.1007/s10444-019-09740-7