Abstract
We construct two novel quaternion-valued smooth compactly supported symmetric orthogonal wavelet (QSCSW) filters of length greater than existing ones. In order to obtain their filter coefficients, we propose an optimization-based method for solving a specific kind of multivariate quadratic equations. This method provides a new idea for solving multivariate quadratic equations and could be applied to construct much longer QSCSW filters.
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Acknowledgements
The authors would like to thank Professor Fritz Keinert for his detailed reply about a Matlab toolbox written by him. We also thank Professor Baobin Li for his useful suggestions. Thank the reviewers for giving us constructive and valuable suggestions.
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Communicated by Hongbo Li
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Jiman Zhao supported by National Natural Science Foundation of China (Grant nos. 11471040 and 11761131002).
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Ma, G., Peng, L. & Zhao, J. Quaternion-Valued Smooth Compactly Supported Orthogonal Wavelets with Symmetry. Adv. Appl. Clifford Algebras 29, 28 (2019). https://doi.org/10.1007/s00006-019-0945-4
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DOI: https://doi.org/10.1007/s00006-019-0945-4