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   -> Volume 6, Issue 10


Answer: Methods to avoid shift variance of WT ? (WD 6.8 #25)
 
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Andrew Dorrell (andrewd@ee.uts.edu.au)
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PostPosted: Sun Sep 28, 1997 1:19 am    
Subject: Answer: Methods to avoid shift variance of WT ? (WD 6.8 #25)
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#20 Answer: Methods to avoid shift variance of WT ? (WD 6.8 #25)

Hi,

I have (perhaps correctly) been harassed for my breivety in answering
a previous question on shift invariance for wavelet transforms. Part
of my reason was that the majority of work I mensioned in my posting
could be found be searching the wavelet digest pages or the internet.
By way of explanation, I do not keep a detailed reference list on all
topics but feel that, if I know some theoretical issues and can pass
on the relevant keywords and search pointers then that may be of use
to the average researcher? However in acknowlegement of my previous
tersness, here is a follow up which will (hopefully) make my
(previous) answer more complete.

Geert Van der Auwera wrote:
>
> Dear Sir,
>
> Some weeks ago I sent you a mail containing the request for some
> references about techniques to overcome the shift-variance of the
> wavelet transformation. I think you are the ideal person to give
> me that information, because you answered a question about this
> subject in the previous Wavelet Digest. I have included it in this
> mail (see below). I would be very grateful if you could send me
> a reference on the following subjects :
>
> - the 'a-trous' algorithm

http://www.obspm.fr/service/sio/docs/html/doc/94NOV/vol2/node329.html
(thanks AltaVista)
Consider also:
[Rio.,Duh.'92] O.Rioul, P. Duhamel, "Fast Algorithms for Discrete and
Continuous Wavelet Transforms", IEEE Trans. on Inf. Theory, vol. 38,
no.2, March 1992,

[She.'92] M.J.Shensa, "The Discrete Wavelet Transform: Weding the A
Trous and Mallat Algorithms", IEEE Trans. on Signal
Proc. vol. 40, no.10, October 1992,

> - the web page of Eero Simoncelli
http://www.cis.upenn.edu/~eero/home.html
http://www.wavelet.org/wavelet/digest_04/digest_04.10.html#8

> - retaining odd and even samples
http://www.wavelet.org/wavelet/digest_06/digest_06.02.html#4

> - any other technique that might be important
Besides Daubechies book, the following talks about shift invariant
frames:
http://www.wavelet.org/wavelet/digest_06/digest_06.08.html#3

Some good references in the context of pattern recognition:
http://www.wavelet.org/wavelet/digest_05/digest_05.04.html#23

specifically:
R. R. Coifman and D. Donoho, Translation-invariant de-noising, in
Wavelets and Statistics (Eds. A. Antoniadis and G. Oppenheim),
Lecture Note in Statistics, Springer-Verlag, pp.125--150, 1995.

J. Liang and T. W. Parks, A translation-invariant wavelet representation
algorithm with applications, IEEE Trans. Sig. Proc., vol.44, no.2,
pp.225-- 232, 1996.

J.-C. Pesquet, H. Krim, and H. Carfantan, Time invariant orthonormal
wavelet representations, IEEE Trans. Sig. Proc., 1996, to appear.

Mr Andrew Dorrell
School of Electrical Engineering
University of Technology, Sydney
All times are GMT + 1 Hour
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