Construction of Compactly Supported Symmetric Scaling

Construction of Compactly Supported Nonseparable Orthogonal Wavelets of L^2(R^n)

On construction of symmetric compactly supported biorthogonal multiwavelets with short sequences

A novel approach for constructing symmetric compactly supported biorthogonal multiwavelets with short sequences is proposed in this paper. For some symmetric types of biorthogonal multiwavelet systems, starting from the symmetric properties of scaling and wavelet functions, parameterized symmetric forms of polyphase matrices can be derived. Furthermore, according to the matrix equations of the ...

Compactly Supported Orthogonal Symmetric Scaling Functions

Daubechies 5] showed that, except for the Haar function, there exist no compactly supported orthogonal symmetric scaling functions for the dilation q = 2. Nevertheless, such scaling functions do exist for dilations q > 2 (as evidenced by Chui and Lian's construction 3] for q = 3); these functions are the main object of this paper. We construct new symmetric scaling functions and introduce the \...

Parameterization of Bivariate Nonseparable Orthogonal Symmetric Scaling Functions with Short Support

Let I be the 2 × 2 identity matrix, and M a 2 × 2 dilation matrix with M = 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 ...

Construction of a class of trivariate nonseparable compactly supported wavelets with special dilation matrix

We present a method for  the construction of compactlysupported $left (begin{array}{lll}1 & 0 & -1\1 & 1 & 0 \1 &  0 & 1\end{array}right )$-wavelets  under a mild condition. Wavelets inherit thesymmetry of the corresponding scaling function and satisfies thevanishing moment condition originating in the symbols of the scalingfunction. As an application, an  example is  provided.