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Construction of orthonormal multi-wavelets with additional vanishing moments.
- Source :
- Advances in Computational Mathematics; Jan2006, Vol. 24 Issue 1-4, p239-262, 24p
- Publication Year :
- 2006
-
Abstract
- An iterative scheme for constructing compactly supported orthonormal (o.n.) multi-wavelets with vanishing moments of arbitrarily high order is established. Precisely, let φ=[φ<subscript>1</subscript>,. . .,φ<subscript>r</subscript>]<superscript>⊤</superscript> be an r-dimensional o.n. scaling function vector with polynomial preservation of order (p.p.o.) m, and ψ=[ψ<subscript>1</subscript>,. . .,ψ<subscript>r</subscript>]<superscript>⊤</superscript> an o.n. multi-wavelet corresponding to φ, with two-scale symbols P and Q, respectively. Then a new (r+1)-dimensional o.n. scaling function vector φ<superscript>♯</superscript>:=[φ<superscript>⊤</superscript>,φ<subscript>r+1</subscript>]<superscript>⊤</superscript> and some corresponding o.n. multi-wavelet ψ<superscript>♯</superscript> are constructed in such a way that φ<superscript>♯</superscript> has p.p.o.=n>m and their two-scale symbols P<superscript>♯</superscript> and Q<superscript>♯</superscript> are lower and upper triangular block matrices, respectively, without increasing the size of the supports. For instance, for r=1, if we consider the mth order Daubechies o.n. scaling function φ [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10197168
- Volume :
- 24
- Issue :
- 1-4
- Database :
- Complementary Index
- Journal :
- Advances in Computational Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 20514064