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Parameterization of Bivariate Nonseparable Orthogonal Symmetric Scaling Functions with Short Support

【摘要】:Let I be the 2 × 2 identity matrix, and M a 2 × 2 dilation matrix with M2 = 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.

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