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   -> Volume 6, Issue 12


Preprint: Multiwavelet papers by Strela
 
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Vasily Strela (strela@pascal.Dartmouth.EDU)
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PostPosted: Thu Nov 20, 1997 12:40 am    
Subject: Preprint: Multiwavelet papers by Strela
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#5 Preprint: Multiwavelet papers by Strela

"From Wavelets to Multiwavelets"

by Gerlind Plonka and Vasily Strela

This paper gives an overview of recent achievements of the
multiwavelet theory. The construction of multiwavelets is based on a
multiresolution analysis with higher multiplicity generated by a
scaling vector. The basic properties of scaling vectors such as
$L^2$-stability, approximation order and regularity are studied. Most
of the proofs are sketched.

"A Note on Construction of Biorthogonal Multi-scaling Functions"

by Vasily Strela

In many applications biorthogonal wavelets prove to be more efficient
than orthogonal ones. In this note we present a procedure for
constructing biorthogonal multi-scaling functions with any given
approximation order, starting from a low pass multi-filter $H_0$. We
show that dual low pass multi-filter $F_0$ can be found if
$mbox{det}(H_0(z))$ and $mbox{det}(H_0(-z))$ do not have common
roots. We also suggest ``two-scale balancing" as a way to enhance
approximation properties of $F_0(z)$. As an illustration to our
technique we construct multi-scaling functions with various smoothness
biorthogonal to Hermite cubics and a pair of low-pass biorthogonal
multi-filters based on the well known GHM orthogonal example.

These papers, as well as other multiwavelet papers, can be found at

http://math.dartmouth.edu/~strela
or
ftp://euler.math.uni-rostock.de/pub/WWW/gerlind/home1.html
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