Quasi-interpolatory refinable functions and construction of biorthogonal wavelet systems

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We present a new family of compactly supported and symmetric biorthogonal wavelet systems. Each refinement mask in this family has tension parameter omega. When omega = 0, it becomes the minimal length biorthogonal Coifman wavelet system (Wei et al., IEEE Trans Image Proc 7:1000-1013, 1998). Choosing omega 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, A 6.C) (or Daubechies 1992, A 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.
Publisher
SPRINGER
Issue Date
2010-10
Language
English
Article Type
Article
Keywords

COMPACTLY SUPPORTED WAVELETS; ORTHONORMAL BASES; PSEUDO-SPLINES; TRANSFORM; FRAMELETS

Citation

ADVANCES IN COMPUTATIONAL MATHEMATICS, v.33, no.3, pp.255 - 283

ISSN
1019-7168
DOI
10.1007/s10444-009-9129-4
URI
http://hdl.handle.net/10203/95123
Appears in Collection
MA-Journal Papers(저널논문)
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