Workshop on Wavelets


PROGRAM
March 15-19, 2004


March 15, 2004 Monday
10:00 AM - 11:00 AM Guido Weiss - "Expository Lectures on Wavelets I"- Room 199
11:00 AM - 12:00 PM Eric Weber - "Wavelets and Admissible Group Representations" - Room 199
1:00 PM - 2:00 PM Eugenio Hernandez - "Non-Linear Approximation in Sequence Spaces with Applications to Wavelets" - Room 199
2:00 - 3:00 PM Hrvoje Sikic - "One Dimensional Parseval Frames" - Room 199
March 16, 2004 Tuesday
1:00 PM - 2:00 PM Dorin Dutkay - "Trace Formulas in Wavelet Theory" - Room 199
2:00 PM - 3:00 PM Ed Wilson - "Expository Lectures on Wavelets II" - Room 199
3:00 PM - 4:00 PM Mauro Maggioni - "Data Analysis and Applications of Wavelet Packet Algorithms to Hyperspectral Imaging and Pathology" - Room 199
March 17, 2004 Wednesday
10:00 AM - 11:00 AM Damir Bakic - "Construction of General Parseval Frame MRA's Associated with Expanding Integer Maxtrix Dilations" - Room 199
11:00 AM - 12:00 PM Ziemowit Rzeszotnik - "The Norm of the Fourier Transform on Finite Abelian groups" - Room 199
1:00 PM - 2:00 PM Demetrio Labate - "A Unified Approach to Reproducing Function Systems on Locally Compact Abelian Groups" - Room 199
2:00 PM - 3:00 PM Guido Weiss - "Expository Lectures on Wavelets III" - Room 199
March 18, 2004 Thursday
1:00 PM - 2:00 PM Brody Johnson - "Convolutional Frames and the Frame Potential" - Room 199
2:00 PM - 3:00 PM Ed Wilson - "Expository Lectures on Wavelets IV" - Room 199
3:00 PM - 4:00 PM Pete Casazza - "Application of Hilbert Space Frames" - Room 199
March 19, 2004 Friday
10:00 AM - 11:00 AM Manos Papadakis - "Eye-sotropic Wavelets" - Room 199 Abstract: In this talk we will present certain results on an innovative construction of wavelets associated with multiresolution analysis in multidimensions. The main idea is to use the theory of frames in order to construct multiresolution analyses whose scaling functions are isotropic in any number of dimensions. Therefore, our design is clearly non-separable. What we will present is a prototype multiresolution structure, the Shannon-like Radial Frame Multiresolution Analysis. Our design is motivated by the fact that retinal image filtering is free of directional preferences and, according to Marr and other neurophysiologists, can be modeled by linear filtering using isotropic Gaussians. Our multiresolution scheme gives rise to Wavelet Algorithms which use isotropic filters. These algorithms have the ability to detect textures and decompose an image by putting regions with the same textural consistency into the same subband. We will show applications of these algorithms t! o biomedical imaging and we will also provide an overview of non-separable multiresolution design in multidimensions together with an overview of our team's future research program.
11:00 AM - 12:00 PM Josip Derado - Room 199
1:00 PM - 2:00 PM Kanghui Guo - "The Basic Properties of Composite Dilation Wavelets" - Room 199
2:00 PM - 3:00 PM Wang Q. Lim - "The Construction of Wavelets Associated with Two Families of Dilations and Translations" - Room 199
4:00 PM - 4:30 PM Tea - Cupples I - Lounge - "Chris Heil is also a Colloquium Speaker for the Department"
4:30 PM - 5:30 PM Chris Heil - "Quantifying Redundancy in Infinite Dimensions" - Room 199 Abstract: This talk is concerned with frames, which are particular types of sequences in a Hilbert space that have useful basis-like properties even though they may be redundant, or overcomplete. Such redundant systems offer many advantages in applications, such as extra design flexibility or increased stability against noise or data loss. However, while redundancy has a clear qualitative meaning, quantifying redundancy turns out to be a difficult problem. We will review the basic properties of frames, and then introduce the concept of "localized" frames and relate redundancy to localization. As particular corollaries we recover the Nyquist density phenomena for windowed exponentials and Gabor frames, but furthermore extend these to new situations and derive some new properties of those systems.

Washington University in St. Louis
Mathematics Department
Campux Box 1146
St. Louis, MO 63130
Phone: (314) 935-6760   FAX: (314) 935-6839.