Refinement equations play an important role in computer graphics and wavelet analysis. In this paper we investigate multivariate refinement equations associated with a dilation matrix and a finitely… Expand

In this paper we shall study vector cascade algorithms and refinable function vectors with a general isotropic dilation matrix with a perturbed mask in Sobolev spaces.Expand

In applications, it is well known that high smoothness, small support, and high vanishing moments are the three most important properties of a biorthogonal wavelet.Expand

Abstract A characterization of multivariate dual wavelet tight frames for any general dilation matrix is presented in this paper. As an application, Lawton's result on wavelet tight frames inL2( R )… Expand

AbstractThis paper generalizes the mixed extension principle in L2(ℝd) of (Ron and Shen in J. Fourier Anal. Appl. 3:617–637, 1997) to a pair of dual Sobolev spaces Hs(ℝd) and H−s(ℝd). In terms of… Expand

We propose a family of tensor product complex tight framelets TP-CTFn for all integers n > 3 with increasing directionality, where n refers to the number of filters in the underlying one-dimensional complex Tight framelet filter bank.Expand

In this paper we are concerned with the construction of symmetric orthonormal scaling functions with dilation factor d=4, which are symmetric about 0 and 1/6, respectively, and how to construct symmetric wavelets from them.Expand

We show that it is always possible to construct 2rd wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L2(R) and achieve the best possible orders of vanishing moments.Expand