Quaternion-Valued Smooth Compactly Supported Orthogonal Wavelets with Symmetry

  • Guangsheng Ma
  • Lizhong Peng
  • Jiman ZhaoEmail author


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.


Quaternion multiresolution analysis Quaternion wavelet filter Multivariate quadratic equations 

Mathematics Subject Classification

65T60 65Y99 



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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Authors and Affiliations

  1. 1.School of Mathematical Sciences, Key Laboratory of Mathmatics and Complex Systems, Ministry of EducationBeijing Normal UniversityBeijingChina
  2. 2.School of Mathematical SciencesPeking UniversityBeijingChina

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