DIMACS Workshop on Analysis with Wavelets, Signals and Geometry

April 4-6, 2001
DIMACS Center, Rutgers University, Piscataway

Richard Gundy, Rutgers University, gundy@rci.rutgers.edu
Ingrid Daubechies, Princeton University, ingrid@math.princeton.edu
Wim Sweldens, Bell Labs, wim@lucent.com
Guido Weiss, Washington University, guido@math.wustl.edu
Presented under the auspices of the Special Focus on Mathematics and the Foundations of Computer and Information Science.

This workshop will explore new directions in the fields of signal processing and wavelet analysis. We will bring together mathematicians, computer scientists, and engineers for an interdisciplinary exchange of research and problems in new areas of time-scale analysis.

Special attention will be devoted to digital geometry processing. This refers to a new collection of techniques for processing digital data taken from surfaces, or manifolds where the geometry is not flat. For example, data obtained from PET scanners is used to obtain a three-dimensional reconstruction of internal organs. The curvature of the "signal source" presents new quantization problems, different from those that arise in processing sound, images, or video. In each of the latter categories, the data set is taken from a flat section of Euclidean space. For sound, the space is two dimensional, the signal being represented as a function of time; for images, intensity(gray level) is plotted as a function of position in the plane and for video, a third time dimension is added. In each of these cases, the data is adapted to sampling at regular intervals and pixels. Regular sampling schemes are adapted to discrete Fourier analysis, or cascade algorithms using mirror filters. If the data arise from sources with curvature, especially non-constant curvature, new "quadrature" problems arise. These problems have been attacked by second generation wavelet techniques, and these will be one of the subjects of the workshop.

Wavelet analysis is usually understood as harmonic analysis where the emphasis is on time-scale rather than time- frequency. The workshop will bring together some mathematicians working on extensions of the wavelet transform arising from groups other than representations of the affine group. The notion of a "coherent state transform" has unified the decomposition/reconstruction formulas for the windowed Fourier transform and the continuous wavelet transform. The coherent state transform has recently been studied for other groups, some exotic, and others, like the integers, not so exotic. These results will be discussed as part of the workshop. Analysis with wavelets has many facets. One of the participants will discuss multifractals, wavelets, and models for internet traffic. Probabilistic methods in wavelet analysis, minimal characterization of wavelets are two additional topics that will be discussed.

The talks will be scheduled to encourage maximum participation and exchange. The research presentations will be approximately fifty minutes each; there will be tutorial-survey talks and organized panel discussions.

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Document last modified on February 7, 2001.