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   -> Volume 4, Issue 1


Thesis: Local Feature Extraction and Its Applications...
 
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saito@ridgefield.sdr.slb.com (Naoki Saito)
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PostPosted: Thu Jan 01, 1970 12:59 am    
Subject: Thesis: Local Feature Extraction and Its Applications...
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Thesis: Local Feature Extraction and Its Applications...

The following Ph.D. thesis is available via:
1) anonymous ftp
pascal.math.yale.edu:/pub/wavelets/lfeulb[1-5].ps.gz
(These 5 files are in compressed format, i.e., binary files. Uncompress them
by "gunzip" after you copy them.)
or
2) gopher
gopher://yaleinfo.yale.edu:7700/11/Acad-Depts/math/Preprints/Wavelets/lfeulb/
This directory contains lfeulb[1-5].ps (5 PostScript files in ascii format).

This thesis essentially contains all my work (related to wavelets) I did for
last 3~4 years. Since the entire thesis is ~ 250 pages, I would be overwhelmed
if many of you request me to send copies via regular mail or email. So, please
try to get the above PostScript files via ftp or gopher.
If you have any question, please contact me at
saito@ridgefield.sdr.slb.com or saito@math.yale.edu.

Title: Local Feature Extraction and Its Applications Using a Library of Bases
Author: Naoki Saito
Institute: Dept. of Mathematics, Yale University
Advisor: Ronald R. Coifman
Acceptance Date: December, 1994
Abstract:
Extracting relevant features from signals is important for signal analysis
such as compression, noise removal, classification, or regression (prediction).
Often, important features for these problems, such as edges, spikes, or
transients, are characterized by local information in the time (space) domain
and the frequency (wave number) domain.

The conventional techniques are not efficient to extract features localized
simultaneously in the time and frequency domains. These methods include:
the Fourier transform for signal/noise separation,
the Karhunen-Lo`{e}ve transform for compression,
and the linear discriminant analysis for classification.
The features extracted by these methods are of global nature either in time or
in frequency domain so that the interpretation of the results may not be
straightforward. Moreover, some of them require solving the eigenvalue systems
so that they are fragile to outliers or perturbations and are computationally
expensive, i.e., $O(n^3)$, where $n$ is a dimensionality of a signal.

The approach explored here is guided by the emph{best-basis paradigm} which
consists of three steps:
1) select a ``best" basis (or coordinate system) for
the problem at hand from a emph{library of bases} (a fixed yet flexible set of
bases consisting of wavelets, wavelet packets, local trigonometric bases, and
the autocorrelation functions of wavelets),
2) sort the coordinates (features) by ``importance" for the problem at hand
and discard ``unimportant" coordinates, and
3) use these survived coordinates to solve the problem at hand.

What is ``best" and ``important" clearly depends on the problem:
for example, minimizing a description length (or entropy) is important for
signal compression whereas maximizing class separation (or relative entropy
among classes) is important for classification.

These bases ``fill the gap" between the standard Euclidean basis and
the Fourier basis so that they can capture the local features and provide
an array of tools unifying the conventional techniques. Moreover, these tools
provide efficient numerical algorithms, e.g., $O(n [log n]^p)$, where
$p=0,1,2$, depending on the basis.

In present thesis, these methods have been applied usefully to a variety of
problems: simultaneous noise suppression and signal compression,
classification, regression, multiscale edge detection and representation,
and extraction of geological information from acoustic waveforms.

Naoki Saito Schlumberger-Doll Research
Email: saito@ridgefield.sdr.slb.com Old Quarry Road
Voice: (203) 431-5209 Fax: (203) 438-3819 Ridgefield, CT 06877 USA
All times are GMT + 1 Hour
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