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   -> Volume 6, Issue 11

Preprint: Arbitrarily Smooth Orthogonal Nonseparable Wavelets
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"Eugene A. Belogay" (

PostPosted: Thu Oct 23, 1997 5:26 pm    
Subject: Preprint: Arbitrarily Smooth Orthogonal Nonseparable Wavelets
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#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 30332-0160

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: gzip-ped (recommended)
1.4 MB: compress-ed (Unix)
4.9 MB: not compressed, quite big

0.5 MB: uncompressed postscript with no figures
0.8 MB: gzip-ped figures only (enlarged, each on a separate page, sideways)
Your browser will probably decompress the file automatically.

I will email postscript or send hardcopy upon request.

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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