| Parameterization of Bivariate Nonseparable Orthogonal Symmetric Scaling Functions with Short Support |
| Received:June 30, 2008 Revised:January 05, 2009 |
| Key Words:
nonseparable bivariate orthogonal symmetric compactly supported.
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| Fund Project:Supported by the Natural Science Foundation of Guangdong Province (Grant Nos.06105648; 05008289; 032038) and the Doctoral Foundation of Guangdong Province (Grant No.04300917). |
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| Abstract: |
| Let $I$ be the $2\times 2$ identity matrix, and $M$ a $2\times 2$ dilation matrix with $M^2=2I$. First, we present the correlation of the scaling functions with dilation matrix $M$ and $2I$. Then by relating the properties of scaling functions with dilation matrix $2I$ to the properties of scaling functions with dilation matrix $M$, we give a parameterization of a class of bivariate nonseparable orthogonal symmetric compactly supported scaling functions with dilation matrix $M$. Finally, a construction example of nonseparable orthogonal symmetric and compactly supported scaling functions is given. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.04.008 |
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