• Publications
  • Influence
Multivariate refinement equations and convergence of subdivision schemes
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 finitelyExpand
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Vector cascade algorithms and refinable function vectors in Sobolev spaces
  • B. Han
  • Computer Science, Mathematics
  • J. Approx. Theory
  • 1 September 2003
TLDR
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
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Analysis and Construction of Optimal Multivariate Biorthogonal Wavelets with Compact Support
  • B. Han
  • Mathematics, Computer Science
  • SIAM J. Math. Anal.
  • 1 December 1999
TLDR
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
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On Dual Wavelet Tight Frames
  • B. Han
  • Mathematics
  • 1 October 1997
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
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Dual Wavelet Frames and Riesz Bases in Sobolev Spaces
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 ofExpand
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Tensor Product Complex Tight Framelets with Increasing Directionality
TLDR
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
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Quincunx fundamental refinable functions and quincunx biorthogonal wavelets
  • B. Han, R. Jia
  • Computer Science, Mathematics
  • Math. Comput.
  • 2002
TLDR
We analyze the approximation and smoothness properties of quincunx fundamental refinable functions. Expand
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Symmetric orthonormal scaling functions and wavelets with dilation factor 4
  • B. Han
  • Mathematics, Computer Science
  • Adv. Comput. Math.
  • 1 April 1998
TLDR
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
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Construction of multivariate biorthogonal wavelets with arbitrary vanishing moments
TLDR
We present a concrete method to build discrete biorthogonal systems such that the wavelet filters have any number of vanishing moments. Expand
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Multiwavelet Frames from Refinable Function Vectors
  • B. Han, Q. Mo
  • Mathematics, Computer Science
  • Adv. Comput. Math.
  • 1 February 2003
TLDR
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
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