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 2, Issue 5


Wavelets at the Dutch Mathematical Congress
 
images/spacer.gifimages/spacer.gif Reply into Digest
Previous :: Next  
Author Message
Tom H. Koornwinder, Universiteit van Amsterdam, The Netherlands.
Guest





PostPosted: Fri Nov 29, 2002 2:28 pm    
Subject: Wavelets at the Dutch Mathematical Congress
Reply with quote

Wavelets at the Dutch Mathematical Congress

The 29th Dutch Mathematical Congress will be held on April 15 and 16, 1993
at the University of Amsterdam, in the psychology building at Roetersstraat 15.
On Friday afternoon, April 16 one of the mini-symposia (organized by
H.J.A.M. Heijmans and Wim Sweldens) will be on wavelets,
with lectures by A. Cohen, J.-P. Antoine and W. Dahmen.
Furthermore the final (plenary) lecture of the congress will be
delivered by B. Jawerth on a wavelet topic.
The full program of these wavelet activities is given below.

For information about the many other congress activities:
see the last issue of "Mededelingen van het Wiskundig Genootschap"
or send email with request for information to wgcong93@fwi.uva.nl
The secretarial address is Ph. Zijlstra, University of Amsterdam,
Faculty of Mathematics and Computer Science, Plantage Muidergracht 24,
1018 TV Amsterdam, fax 020-525 5101.

Advance registration (preferred) can be done by email before April 5.
Ask for electronic registration form by sending email to wgcong93@fwi.uva.nl
and mention on the subject line the single word
formrequest
Late registration is possible during the congress.


Program of the wavelet activities on April 16

13.45-14.30 A. Cohen (Paris), "Regularity estimates for scaling functions and
wavelets"
14.30-15.15 J.-P. Antoine (Louvain-la-Neuve), "Wavelets, from group theory to
signal and image processing"
15.30-16.15 W. Dahmen (Aachen), "Computing inner products of wavelets"

16.30-17.30 B. Jawerth, "Wavelets on closed sets and applications"


Abstract of A. Cohen's lecture:
In many applications of wavelet bases, e.g. image processing and numerical
analysis, it is important to use a regular wavelet and scaling function.
This requirement leads to the problem of estimating the Holder or Sobolev
exponent of these functions which are in many case obtained as a limit of
a subdivision scheme.
We shall review several existing methods that provide with such estimations,
and we shall discuss their specific advantages and drawbacks.
Several related open problems will be raised.

Abstract of J.-P. Antoine's lecture:
The n-dimensional Continuous Wavelet Transform (CWT) is ultimately
rooted in group theory, since it is based on a square integrable
representation of the similitude group of R^n, which in one dimension
reduces to the connected affine group of the line or $ax+b$-group.
From this all the relevant formulas follow: energy conservation,
reproducing kernel, reconstruction formula, etc. In addition, the
parameter space of the CWT may be considered as a phase space, i.e., a
co-adjoint orbit of the corresponding group. In addition to the general
abstract theory just outlined, special emphasis will be put on the
reproducing kernel, both from the conceptual point of view and for
practical implementation (discretization problems, resolving power of
the CWT). Finally, a comparison will be made between the CWT and the
familiar discrete or dyadic transform.

Abstract of W. Dahmen's lecture:
In many applications of wavelet bases, e.g. image processing and numerical
analysis, it is important to use a regular wavelet and scaling function.
This requirement leads to the problem of estimating the Holder or Sobolev
exponent of these functions which are in many case obtained as a limit of
a subdivision scheme.
We shall review several existing methods that provide with such estimations,
and we shall discuss their specific advantages and drawbacks.
Several related open problems will be raised.

Abstract of B. Jawerth's lecture:
Multiscale analysis comes with a natural hierarchical structure obtained by
only considering the linear combinations of building blocks up to a certain
scale. This hierarchical structure is particularly suited for fast numerical
implementations; the underlying idea being that functions on a certain
scale only need to be sampled at a rate approximately given by the scale they
live on. This hierarchical structure is easy to turn into a fast
numerical algorithm for calculating the wavelet transform.
In this lecture we shall discuss procedures which utilize
the inherent hierarchical structure in a different way. These procedures share
the feature that they involve probing and gathering information from
several different scales while keeping the location (essentially) fixed.
Typically, they lead to numerical algorithms which are very fast, with a
complexity proportional to the number of levels being processed.
There are a number of examples of this kind of ``wavelet probing."
The one we shall consider in greatest detail is the construction of wavelets
on closed subsets. We shall also show how similar ideas lead to extremely quick
algorithms for splitting and merging functions.
Splitting allows us to find the wavelet coefficients associated with
different subsets of a function originally defined on a larger
set. Merging goes in the opposite direction and involves starting with
the wavelet coefficients on the smaller sets and finding the wavelet
coefficients associated with the the union of the sets.
Other examples we shall discuss briefly are algorithms for very quick,
smoothness preserving extensions of functions, pointwise evaluation of
wavelet decompositions, and edge detection.
We shall present applications of these ideas to image compression and
to compression of matrices, and also show how they readily lead to algorithms
perfectly suited for massively parallel environments.
All times are GMT + 1 Hour
Page 1 of 1

 
Jump to: 
 


disclaimer - webmaster@wavelet.org
Powered by phpBB

This page was created in 0.026702 seconds : 18 queries executed : GZIP compression disabled