A method for constructing trivariate nonseparable compactly supported orthogonal wavelets

Abstract

We first introduce trivariate multiresolution analysis and trivariate orthogonal wavlets. We then give a method for constructing a class of trivariate nonseparable compactly supported orthogonal scaling functions and the related wavelets. Finally, we study the regularity of these wavelets. We can get arbitrarily smooth trivariate orthogonal wavelets.

Keywords:

• multiresolution analysis
• trivariate orthogonal wavelets
• regularity
• low-pass filter
• high-pass filter

2000 AMS Subject Classification :

• 42C40
• 65T60

Acknowledgements

The authors would like to thank the referees for their valuable comments and suggestions.