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   -> Volume 7, Issue 3


Answer: Wavelets and integral equations in 2 and 3D (WD 5.2 #28)
 
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Andrew Dorrell (andrewd@ee.uts.edu.au)
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PostPosted: Tue Feb 17, 1998 6:50 am    
Subject: Answer: Wavelets and integral equations in 2 and 3D (WD 5.2 #28)
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#15 Answer: Wavelets and integral equations in 2 and 3D (WD 5.2 #28)

Ingve Simonsen wrote:
>
> Dear Andrew
>
> In the Wavelet Digest 1996 you had the following question:
>
> >Dear waveleters,
> >
> >In G. Beylkin, R. Coifman and V. Rokhlin, "Fast Wavelet Transforms and
> >Numerical Algorithms I.", the authors describe techniques for applying
> >operators to one dimensional data in the wavelet domain. They also
> >note that extension to higher dimensions is relatively
> >straightforward.
> >
> >I am interested in knowing if anyone has implemented these techniques >in
> >2D or 3D. Alternatively, what literature might be available describing
> >how this could be done?
> >
> >Thanks in advance,
> >
> >Mr Andrew Dorrell
> >email: andrewd@ee.uts.edu.au
>
> I an curious what kind of answers (if any) you got. Any references codes
> etc.

The only answers I got were ones like your own icon_sad.gif So I had to work
out the details myself and they form a component of my thesis which is
now being vetted prior to final submission.

In short the computational characteristics are pretty nasty when you
use the regular ND transform structure which is separable only over
one level. Of course they are similar to the BCR case when the N
level transform is applied to rows then columns of the data (ie. in
completely separable fashion)

If you are interested in more detail I can find out what the
publication policy of UTS is for theses --- ie how soon I will be able
to publish my thesis globally. I can't really say whether I will be
publishing a paper covering the work at this stage.
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