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   -> Volume 4, Issue 9

Video: Martin Marietta Wavelets Workshop II October 4-6, 1993
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PostPosted: Fri Dec 06, 2002 9:33 am    
Subject: Video: Martin Marietta Wavelets Workshop II October 4-6, 1993
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Video: Martin Marietta Wavelets Workshop II October 4-6, 1993

Martin Marietta Wavelets Workshop II October 4-6, 1993

Fast Mathematical Algorithms and Hardware (FMA&H) is pleased to offer
versions of their video taped workshop on wavelets presented at the
Orlando Lockheed Martin facility with minor editing. The lectures are
designed for Engineers, Signal Processing and Government Labs
personnel. They make excellent resource material and can be used as
addendum to graduate level courses in wavelet signal processing.
Although a strong mathematical background is not assumed, accuracy is
not compromised.


Wavelets is a generic name for a collection of localized waveforms
used in signal processing. By correlating signals with appropriately
chosen wavelets, certain analysis tasks such as feature extraction,
signal compression, denoising and recognition can be facilitated. As
part of these lectures, Drs. Coifman and Wickerhauser demonstrate
these tasks using the software from one of our toolkits called the
Wavelet Packet Library for Windows (WPLW), where the main tasks for
the wavelet based toolkit is feature extraction, denoising and

Wavelet analysis provides a simple comprehensive mathematical and
algorithmic infrastructure. In addition, it has provided many new
tools which evolved as a result of the cross fertilization of ideas
from many fields, such as Calderon-Zygmund theory in mathematics,
seismic prospecting, mathematical physics, wave packets, pyramid
structures in image processing, band and subband filtering in signal
processing, music, etc. Rather than elaborate on the origin of these
ideas Dr. Coifman discusses and shows examples of the current state of
this elaborate toolkit and the relative advantages it brings to the
signal analysis scene.


There are 11 tapes with minor editing in this series of lectures. You
can purchase these tapes in several ways according to your personal

1. In totality (entire set),
2. By grouping according to Lecturer (all of Professor Coifman's
tapes, etc.)
3. By individual tape.

In addition, we will have in the near future the set of lectures from
the 1991 workshop that featured, in addition to Professors Coifman and
Wickerhauser, Professor Stephane Mallat from the Courant Institute at

For more information contact Charles Stirman at
telephone(407)-644-6236 or
Ms. Marie Kissinger at (210)-659-1818.

To purchase these tapes, please submit your order along with your
payment either a Money Order or Cashiers Check in US Dollars payable

FMA&H, Inc.
1020 Sherman Avenue
Hamden, CT 06514

Indicate on your order the Tape Number(s) or Entire Set. Note that
lectures 3 and 4 by Dr. Rudin are on one tape (tape 3). The cost is
$25.00 per tape or $220.00 for the entire set plus $6.95 for postage
and handling within the continental United States. For foreign orders,
please contact Charles Stirman or Marie Kissinger for postage and
handling prior to placing your order. We will reconfirm your purchase
request. Allow 2 weeks for delivery within the continental United
States and 4 weeks for overseas delivery. For the first 200 orders
received we will include the lecture notes from Drs. Coifman and
Wickerhauser at no extra cost.


The following is a brief synopsis giving the video tape number,
lecture number, lecturer, title and a brief description of some of the
topics covered.

Tape 1 - Lecture 1 - 58 minutes - Dr. Ronald Coifman.
Title: Introduction

Dr. Coifman presents an introduction to the entire series by
discussing the goals of feature extraction and denoising. Included are
examples from Magnetic Resonance Imaging, Radar and Acoustics. Broad
descriptions of problems and solutions with minimal mathematics is
provided and the notion of a ``Best Basis" which optimizes a desired
characteristic (such as minimal encoding length or minimal error rate
in classification) is introduced.

Tape 2 - Lecture 2 - 78 minutes - Dr. Ronald Coifman
Title: Software toolkit for one dimension

Dr. Coifman demonstrates the WPLW software for signal processing in
one dimension. Included is a demonstration of techniques for
extracting dominant components from the wavelet transform of a
function. Then the function is reconstructed from its dominant
components, using a library of basis functions.

Examples include:
1. analysis of linear and quadratic chirps using Haar waveforms as
well as smoother filters.
2. discussion of the FBI's fingerprint storage problem (The JPEG
standard, and the compression problem).
3. Reintroduction of missing features in images by working in
transform domain.

Tape 3 - Lecture 3 - 60 minutes - Dr. Lenny Rudin
Title: Fast algorithm for clutter removal through pyramidal segmentation

Dr. Rudin discusses the challenges of Automatic Target Recognition
followed by discussions on textures and clutter, Piece wise Constant
Multi-scale Segmentation, the effects of filtering on each scale,
Least Squares Piecewise Polynomial Segmentation, Centroiding and the
applications of these topics to Forensics

Tape 3 - Lecture 4 - 57 minutes - Dr. Lenny Rudin
Title: Application of nonlinear partial differential equations to image

Dr. Rudin discusses nonlinear multi-scale analysis through nonlinear
partial differential equations for image enhancement. He describes a
modern variational approach to image domain segmentation and
decluttering. He argues that one of the main uses is in abstracting
objects from camouflage such as terrain, foliage, or anything that
engulfs objects and detracts from the image. He discusses image
domain restoration using modern variation approaches such as linear,
nonlinear and total variation (TV) based methods including TV based
restoration of noisy blurred images with local constraints.

Tape 4 - Lecture 5 - 70 minutes - Dr. Victor Wickerhauser
Title: The Basics of how to choose wavelets

Dr. Wickerhauser describes the basics of wavelet construction, local
Cosines in the context of Best Basis, a fast wavelet transform using
proper wavelet construction, Haar wavelets and Haar wavelet packets.
He also discusses the efficiency of representations of signals;
adapting waveforms to signals, time-frequency atomic bases and the
Heisenberg uncertainty principle and functional, characteristics of
the Daubechies wavelets and the Mallat algorithm.

Tape 5 - Lecture 6 - 90 minutes - Dr. Victor Wickerhauser
Title: Tailoring wavelets and FAST analysis

Dr. Wickerhauser discusses seven tailoring wavelets: adapted waveform,
multidimensional wavelets, wavelets on the interval, correlation of
signals, fast front end for Karhunen-Loeve decomposition, most
distinguishing basis and, approximate Jacobeans. Each of these
wavelets are concisely analyzed to give a the viewer a foundation to
build upon and infer from.

Tape 6 - Lecture 7 - 85 minutes - Dr. David Donoho
Title: Nonlinear Wavelet Methods for Recovery of Signals, Densities, and
Spectra from Indirect and Noisy Data

Dr. Donoho discusses (1) Wavelet denoising, (2) Wavelet approaches to
linear inverse problems, (3) Wavelet Packet denoising, (4) segmented
multiresolutions, and (5) nonlinear multiresolutions. The common
ideas focus on utilizing nonlinear options in the wavelet domain. The
new methods in this video accomplish tasks which are not possible by
traditional linear/Fourier approaches.

Tape 7 - Lecture 8 - 80 minutes - Dr. David Donoho
Title: Wavelet Shrinkage

Dr. Donoho describes the mechanics of wavelet shrinkage techniques and
gives examples to further familiarize the viewer with the techniques.
The techniques involve denoising by (1) soft thresholding, (2)
discrete inverse problems, (3) numerical differencing, (4)
discrete-time deconvolution, and (5) continuous inverse problems.

Tape 8 - Lecture 9 - 55 minutes - Dr. Gregory Beylkin
Title: An Approach to Compression and Fast Processing of Synthetic Aperture
Radar (SAR) Data

Dr. Beylkin discusses how both SAR and Seismic data processing
mathematical models used for one another in analysis of operators,
results in a matched data filtering technique. In developing this
technique, Dr. Beylkin considers for application to SAR processing
several simplified mathematical models which were originally developed
for seismic processing. Through the developing process, he discusses
(1) Zero-Offset configurations in SAR and seismic exploration, (2) A
simplified model for SAR data processing, (3) an operator in X-W
domain, and (4) compression of SAR and seismic data.

Tape 9 - Lecture 10 - 82 minutes - Dr. Victor Wickerhauser
Title: Picture compression

Dr. Wickerhauser discusses image compression techniques including: the
JPEG standard (description and theoretical basis); local cosine
transform (LCT) compression ( description and theory); Bell functions
for the LCT; Subband coding schemes: wavelet decomposition, wavelet
packet decomposition, and weak orthogonal octave subband
multiresolution decomposition. He also covers the cost of computing
and storing best bases for individual images, the efficient use of
memory in the Best Basis algorithm, storing video images and,
calculating the Karhunen-Loeve transform of a 3 channel (red, green,
blue) signal.

Tape 10 - Lecture 11 - 51 minutes - Dr. Victor Wickerhauser
Title: New Tools for DSP

Dr. Wickerhauser, shares his abundant knowledge of "The local cosine
trick", a fast local cosine transform, folding and unfolding
technique, a "trick" to periodize smooth functions smoothly, the
basics in using folding, the best basis algorithm for the local cosine
bases, matrix multiplication using wave packet/local cosine bases and
the best basis algorithm, and parallelizing 2-dimensional wavelet

Tape 11 - Lecture 12 - 80 minutes - Dr. Ronald Coifman
Title: New wavelet packet software

In this last lecture of the series, Dr. Coifman discusses denoising
and feature extraction: building a model of a signal examples using
wavelet packet software; representation of acoustic scattering matrix
in local cosine basis; and the future use of best basis techniques for
classification problems.
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