2D wavelet followed by 2D FFT?

I am having trouble understanding the meaning of an operation that a
customer finds useful.

They have a 2D block of data that is part of a medical image.

They do a 2D wavelet transform on this, followed by a 2D FFT of the
wavelet coefficient set.

I find it hard to visualize what the result of this means.

Any sugestions would be welcome.

Thanks,

Chris
===========================
Chris Bore
BORES Signal Processing
www.bores.com

On Oct 15, 1:09&#4294967295;pm, Chris Bore <chris.b...@gmail.com> wrote:
> I am having trouble understanding the meaning of an operation that a
> customer finds useful.
>
> They have a 2D block of data that is part of a medical image.
>
> They do a 2D wavelet transform on this, followed by a 2D FFT of the
> wavelet coefficient set.
>
> I find it hard to visualize what the result of this means.
>
> Any sugestions would be welcome.
>
> Thanks,
>
> Chris
> ===========================
> Chris Bore
> BORES Signal Processingwww.bores.com

2D Wavelet transform gives sub sampled signals in spatial domain
separated into different.scales in different directions
Applying FFT on the wavelet coefficients we can analyze frequency
spectrum in different zones and different directions.

In article 
<cd299d90-25a7-4389-93fc-c519edefb2f2@u40g2000pru.googlegroups.com>,
 Chris Bore <chris.bore@gmail.com> wrote:

> I am having trouble understanding the meaning of an operation that a
> customer finds useful.
> 
> They have a 2D block of data that is part of a medical image.
> 
> They do a 2D wavelet transform on this, followed by a 2D FFT of the
> wavelet coefficient set.
> 
> I find it hard to visualize what the result of this means.
> 
> Any sugestions would be welcome.

This would make sense to me only if the the FFT was taken over 
individual subbands.  For example, a 2-level wavelet transform would 
result in 7 sub-FFTs:

3 - N/2 x N/2 FFTs
4 - N/4 x N/4 FFTs

Even then, I'm not sure how useful this would be, as the FFT would only 
serve to confirm that the wavelet transform was successful in separating 
horizontal, vertical, and diagonal information.

There is no way you would want to do this over the entire 
wavelet-transformed image as the energy at the borders of the subbands 
would dominate the the FFT.

Ken Prager

Chris Bore wrote:

> I am having trouble understanding the meaning of an operation
> that a customer finds useful.

Useful how? Is that undisclosable or haven't they told you?

> They have a 2D block of data that is part of a medical image.
> 
> They do a 2D wavelet transform on this, followed by a 2D FFT of
> the wavelet coefficient set.

Perhaps it's analogous to the cepstrum which analyzes periodicities 
in the spectrum, like harmonic series. Repetitive behavior across 
scales would seem to indicate self-similarity in the space-domain 
signal. (Fractal dimension of the capillary system? ;)


Martin

-- 
  The more you can say with a language,
the less you can say about the language.
--Kathy Yellick

On Oct 15, 3:18&#4294967295;pm, Martin Eisenberg <martin.eisenb...@udo.edu> wrote:
> Chris Bore wrote:
> > I am having trouble understanding the meaning of an operation
> > that a customer finds useful.
>
> Useful how? Is that undisclosable or haven't they told you?

Undiscosable. Definitely useful, proven empirically. I am trying to
understand what it does, and possibly to show that it is analogous to
some other operation that is more common.

>
> > They have a 2D block of data that is part of a medical image.
>
> > They do a 2D wavelet transform on this, followed by a 2D FFT of
> > the wavelet coefficient set.
>
> Perhaps it's analogous to the cepstrum which analyzes periodicities
> in the spectrum, like harmonic series. Repetitive behavior across
> scales would seem to indicate self-similarity in the space-domain
> signal. (Fractal dimension of the capillary system? ;)


That sounds productive. Thanks.

>
> Martin
>
> --
> &#4294967295; The more you can say with a language,
> the less you can say about the language.
> --Kathy Yellick