No Title

Wavelets: The Latest Big Splash in
Science, Engineering, Imaging and Graphics

A half-day symposium at the
American Association for the Advancement of Science
Annual Meeting and Science Innovation Exposition

Tuesday, 17th February 1998

Philadelphia Marriott, Grand Ballroom I

9:00am-12:00 noon

Organizers:

Colm Mulcahy

Associate Professor of Mathematics
Spelman College
Atlanta, GA 30314
(404) 223-7627 (ph), (404) 223-7662 (fax)
colm@spelman.edu
http://www.spelman.edu/~colm

Farid Dowla

Research Engineer, Computational Physics Group
Lawrence Livermore National Laboratory
7000 East Ave., Livermore, CA 94550
(510) 423-7579 (ph), (510) 423-4077 (fax)
dowla@s75.es.llnl.gov
http://www.llnl.gov/das/wavelet/wavelet.html

Rationale:

Wavelets are acquiring an ever-increasing visibility and popularity in the scientific world because of the extraordinary range of their applications. A relatively new arrival on the mathematical scene, one of the attractions of wavelets is that they provide an alternative to classical Fourier methods for both one- and multi-dimensional data analysis and synthesis. They are particularly useful in the context of transient signals, because of the localization properties of the basis functions used in the transform.

Fields as diverse as seismology, image processing, signal processing, data storage/transmission/compression, computer graphics, and biological and medical imaging have all benefited substantially from recent advances in wavelets. Frontier technologies such as effective video conferencing will surely transform society significantly once they are in place, are about to take quantum leaps forward thanks to innovative wavelet based algorithms, which are fast and simple.

This symposium will introduce the mathematical basics of wavelets, and present cutting-edge and emerging applications in four main areas: signal processing, data and communication technology, computer graphics and biomedical imaging. Many of these applications cross discipline boundaries, and serve to reinforce the unifying nature of some of the best of today's research.

Speakers and abstracts:

Gilbert Strang (MIT)

AN INTRODUCTION TO WAVELETS

Professor of Mathematics
Massachusetts Institute of Technology
Cambridge, MA 02139
(617) 253-4383 (ph), (617) 253-4358 (fax)
gs@math.mit.edu
http://www-math.mit.edu/~gs

``Wavelets are remarkable functions, but at first their construction looked complicated. They have several crucial properties at once: 1. Finite length, 2. Orthogonality and 3. Good approximation. The finite length means that the information from wavelets is local. In Fourier series, a jump in the function affects all the coefficients and produces ripples (the Gibbs phenomenon). With wavelets, the coefficients tell directly when and where the jump occurred. Orthogonality means as always that computing the coefficients is much simplified. For wavelets this step is particularly neat. The approximation property allows a small number of wavelet terms to come close to an arbitrary signal or image. All these desirable properties come at a price. This introductory lecture will explain that price: the key idea of filtering and sampling a signal. Good wavelets require a good choice of filter. This choice is now much easier to make - and the remarkable functions that appear have a wide range of applications. The key idea is to separate the big picture from the details (at several levels!). We try to achieve this `multiresolution' in our lecture too.''

Prof. Strang is known for his ability to introduce a general audience to this sophisticated branch of mathematics in a gradual and gentle manner, as witnessed by his American Scientist article [14]. He will give an overview of the mathematical basics of wavelets drawing on the ideas explored there, as well a recent text he co-authored [15].

This talk will prepare attendees from all walks of scientific life for the applications-oriented presentations that follow.

Björn Jawerth (Summus Ltd. and University of South Carolina)

LET YOUR WAVELETS DO THE WALKING...AN INTRODUCTION TO
IMAGING AND INFORMATION ACCESS

Chief Technical Officer, Summus, Ltd.
950 Lake Murray Blvd., Irmo, SC 29063
(803) 781-5674 (ph), (803) 781-5679 (fax)
bj@summus.com
http://www.summus.com

David W. Robinson Palmetto Professor of Mathematics
University of South Carolina
Columbia, SC 29208

``Society as a whole depends on the distribution and exchange of information, and progress is now, more than ever before, relying on our ability to control and access the information flow in an efficient way. Wavelets provide useful techniques for this in several different ways and wavelets are now part of a host of emerging applications and technologies. I'll discuss a broad spectrum of questions concerning wavelets and information access, ranging from theoretical considerations to the latest commercial applications, including sound/image/video compression and transmission, digital cameras, photo IDs and fingerprints, and low bandwidth applications on the internet.''

Live demos of video conferencing over the telephone, and video and still images on the internet, will be featured (see [18, 19, 20, 21]).

Farid Dowla (Lawrence Livermore)

THE WAVELET TRANSFORM: THE NATURAL ALGORITHM IN SEISMIC SIGNAL ANALYSIS

``One of the first fields to profit from wavelet methods was signal processing. Wavelet design for a particular type of data is of significant interest in adaptive signal processing for noise cancellation, feature detection, and data compression. How can we design wavelets that `look' very different from each other and yet possess the properties of the common orthogonal and biorthogonal wavelets?''

Dr. Dowla will discuss in clear and simple terms methods of designing wavelets based on the spectral and temporal characteristics of real signals and images. Starting with examples of real data from seismic, biomedical and communication applications, various recent methods of wavelet design, and their effect on signal and image processing algorithms will be considered [22, 23, 24, 25].

Dennis M. Healy Jr. (DARPA and Dartmouth College)

ADAPTED WAVELETS IN MEDICINE AND BIOLOGY: EXAMPLES FROM
IMAGING, SIGNAL PROCESSING, AND MOLECULAR STRUCTURE COMPUTATIONS

Program Manager, Applied and Computational Mathematics Program
Defense Advanced Research Projects Agency
Arlington, VA 22203-1714
(703) 696-0143 (ph)
dhealy@darpa.mil

Associate Professor of Mathematics and of Computer Science
Dartmouth College, Hanover, NH 03755
http://www.cs.dartmouth.edu/~healy

``Biomedical science and engineering offer a spectrum of exciting challenges and opportunities for the application of recent advances in scientific computation and signal processing. For instance, interesting problems attend numerous aspects of medical imaging; in data acquisition for various medical imaging modalities, compression of images for archiving and transmission, image enhancement, and diagnostic cuing. In biochemistry, opportunities may be found in the structure problem in crystallography or in macromolecular structure computation for rational drug design. Wavelets and related techniques play a growing role; see the books Wavelets in Medicine and Biology [27], Time-Frequency Methods in the Engineering and Biological Sciences [26], or a recent special issue of Annals of Biomedical Engineering [28]. In imaging, these tools have been applied to speeding up the acquisition of Magnetic Resonance Imaging (MRI), while reducing artifacts and noise, enhancements in MRI spectroscopy, reducing radiation exposure in Computer Tomography (CT), and improving blood flow velocimetry.''

Dr. Healy will survey this area, presenting some of the imaging and enhancement work done by his group since 1989, as well as some of the exciting developments in the broader community. A brief discussion of DARPA's efforts in macromolecular structure computation will also be given.

Adam Finkelstein (Princeton University)

WAVELETS IN COMPUTER GRAPHICS: THE COLOR, SIZE AND SHAPE OF THINGS

Assistant Professor of Computer Science
Princeton University
Princeton, NJ 08544-2087
609/258-5756 (ph), 609/258-1771 (fax)
af@princeton.edu
http://www.cs.princeton.edu/~af

``Computer graphics [31] is currently enjoying an explosion in public awareness due to the advent of the World Wide Web, performance advances and proliferation of PCs, and Hollywood. The revolution of digital media and the rise of popular interest in computer graphics have created a demand for new classes of applications for creation, modification, distribution, protection, and searching for these media. Wavelet analysis - a tool that has recently emerged from the mathematical community - has been effectively applied in a variety of disciplines that grapple with large collections of data. This talk surveys a number of applications for wavelet analysis in computer graphics [32, 33, 34, 35, 36]. I will describe a multiresolution representation of images and how it can be used to create, manipulate and compress images with different levels of detail in different places, as well as how it can be used to quickly find an image in a large database. I will also show how wavelets can be used to create, display, and manipulate 2D and 3D shapes, as well as video. ''

References