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Construction of orthonormal multi-wavelets with additional vanishing moments. (English) Zbl 1115.65133
In this interesting paper, an iterative scheme for constructing compactly supported orthonormal multiwavelets with vanishing moments of arbitrarily high order is established. Precisely, let $\varphi ={\left({\varphi }_{1},...,{\varphi }_{r}\right)}^{T}$ be an $r$-dimensional orthonormal scaling function vector with polynomial preservation of order $m$, and $\psi ={\left({\psi }_{1},...,{\psi }_{r}\right)}^{T}$ an orthonormal multiwavelet corresponding to $\varphi$, with two-scale symbols $P$ and $Q$, respectively. Then a new $\left(r+1\right)$-dimensional orthonormal scaling function vector ${\varphi }^{*}={\left({\varphi }^{T},{\varphi }_{r+1}\right)}^{T}$ and some corresponding orthonormal multiwavelet ${\psi }^{*}$ are constructed in such a way that ${\varphi }^{*}$ has polynomial preservation of order $n>m$ and their two-scale symbols ${P}^{*}$ and ${Q}^{*}$ are lower and upper triangular block matrices, respectively, without increasing the size of the supports. This method is illustrated by some examples.
MSC:
 65T60 Wavelets (numerical methods) 42C40 Wavelets and other special systems 42C15 General harmonic expansions, frames
References:
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