The Wavelet Digest Homepage
Return to the homepage
Search the complete Wavelet Digest database
Help about the Wavelet Digest mailing list
About the Wavelet Digest
The Digest The Community
 Latest Issue  Back Issues  Events  Gallery
The Wavelet Digest
   -> Volume 6, Issue 11

Preprint: Arbitrarily Smooth Orthogonal Nonseparable Wavelets
images/spacer.gifimages/spacer.gif Reply into Digest
Previous :: Next  
Author Message
"Eugene A. Belogay" (

PostPosted: Thu Oct 23, 1997 5:26 pm    
Subject: Preprint: Arbitrarily Smooth Orthogonal Nonseparable Wavelets
Reply with quote

#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
All times are GMT + 1 Hour
Page 1 of 1

Jump to: 

disclaimer -
Powered by phpBB

This page was created in 0.024612 seconds : 18 queries executed : GZIP compression disabled