Construction of orthonormal multi-wavelets with additional vanishing moments
Authors: Chui, Charles; Lian, Jian-ao
Source: Advances in Computational Mathematics, Volume 24, Numbers 1-4, January 2006 , pp. 239-262(24)
Abstract:An iterative scheme for constructing compactly supported orthonormal (o.n.) multi-wavelets with vanishing moments of arbitrarily high order is established. Precisely, let =[1,. . .,r]⊤ be an r-dimensional o.n. scaling function vector with polynomial preservation of order (p.p.o.) m, and =[1,. . .,r]⊤ an o.n. multi-wavelet corresponding to , with two-scale symbols P and Q, respectively. Then a new (r+1)-dimensional o.n. scaling function vector #:=[⊤,r+1]⊤ and some corresponding o.n. multi-wavelet # are constructed in such a way that # has p.p.o.=n>m and their two-scale symbols P# and Q# 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 mD, then #:=[mD,2]⊤ is a scaling function vector with p.p.o. >m. As another example, for r=2, if we use the symmetric o.n. scaling function vector in our earlier work, then we obtain a new pair of scaling function vector #=[⊤,3]⊤ and multi-wavelet # that not only increase the order of vanishing moments but also preserve symmetry.
Document Type: Research Article
Publication date: January 1, 2006