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> Volume 6, Issue 11
Preprint: Arbitrarily Smooth Orthogonal Nonseparable Wavelets

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"Eugene A. Belogay" (ebelogay@math.gatech.edu) Guest

Posted: Thu Oct 23, 1997 5:26 pm Subject: Preprint: Arbitrarily Smooth Orthogonal Nonseparable Wavelets




#7 Preprint: Arbitrarily Smooth Orthogonal Nonseparable Wavelets
Subject: Preprint: Arbitrarily Smooth Orthogonal Nonseparable Wavelets
Title: Arbitrarily Smooth Orthogonal Nonseparable Wavelets In $R^2$
Authors: Eugene Belogay and Yang Wang
School of Mathematics
Georgia Institute of Technology
Atlanta GA 303320160
Abstract: For each positive integer $r$ we construct a family of
bivariate orthogonal wavelets with compact support that are
nonseparable and have vanishing moments of order $r$ or less. The
starting point of the construction is a scaling function that
satisfies a dilation equation with special coefficients and special
dilation matrix $M$: the coefficients are aligned along two adjacent
rows and $det M=2$. We prove that if $M=[0 2; 1 0]$, then the
smoothness of the wavelets improves asymptotically by $1  (log_2
3)/2 approx 0.2075$ when $r$ is incremented by 1. Hence they can be
made arbitrarily smooth by choosing $r$ large enough.
Keywords: Nonseparable wavelets, smooth orthogonal scaling function, regularity
Postscript: Differently compressed versions are available by anonymous ftp
(just point your web browser).
0.9 MB: gzipped (recommended)
ftp://ftp.math.gatech.edu/pub/users/ebelogay/pub/nonsepar.ps.gz
1.4 MB: compressed (Unix)
ftp://ftp.math.gatech.edu/pub/users/ebelogay/pub/nonsepar.ps.Z
4.9 MB: not compressed, quite big
ftp://ftp.math.gatech.edu/pub/users/ebelogay/pub/nonsepar.ps
0.5 MB: uncompressed postscript with no figures
ftp://ftp.math.gatech.edu/pub/users/ebelogay/pub/nonsep0.ps
0.8 MB: gzipped figures only (enlarged, each on a separate page, sideways)
ftp://ftp.math.gatech.edu/pub/users/ebelogay/pub/nonsepfig.ps.gz
Your browser will probably decompress the file automatically.
I will email postscript or send hardcopy upon request.
ebelogay@math.gatech.edu
Filter coefficients: The manuscript describes an explicit procedure to
compute the scaling/wavelet coefficients, but you will need to use
some spectral factorization software. I hope to post numerical
coefficients in different formats soon.
Eugene Belogay 





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