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Quasi-interpolatory refinable functions and construction of biorthogonal wavelet systems

Title
Quasi-interpolatory refinable functions and construction of biorthogonal wavelet systems
Authors
Kim H.O.Kim R.Y.Lee Y.J.Yoon J.
Ewha Authors
윤정호
SCOPUS Author ID
윤정호scopus
Issue Date
2010
Journal Title
Advances in Computational Mathematics
ISSN
1019-7168JCR Link
Citation
vol. 33, no. 3, pp. 255 - 283
Indexed
SCIE; SCOPUS WOS scopus
Abstract
We present a new family of compactly supported and symmetric biorthogonal wavelet systems. Each refinement mask in this family has tension parameter ω. When ω = 0, it becomes the minimal length biorthogonal Coifman wavelet system (Wei et al., IEEE Trans Image Proc 7:1000-1013, 1998). Choosing ω away from zero, we can get better smoothness of the refinable functions at the expense of slightly larger support. Though the construction of the new biorthogonal wavelet systems, in fact, starts from a new class of quasi-interpolatory subdivision schemes, we find that the refinement masks accidently coincide with the ones by Cohen et al. (Comm Pure Appl Math 45:485-560, 1992, §6.C) (or Daubechies 1992, §8.3.5), which are designed for the purpose of generating biorthogonal wavelets close to orthonormal cases. However, the corresponding mathematical analysis is yet to be provided. In this study, we highlight the connection between the quasi-interpolatory subdivision schemes and the masks by Cohen, Daubechies and Feauveau, and then we study the fundamental properties of the new biorthogonal wavelet systems such as regularity, stability, linear independence and accuracy. © 2009 Springer Science+Business Media, LLC.
DOI
10.1007/s10444-009-9129-4
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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