Dewey S. Tucker
Learning Multiscale Models from Data
Previous research in multiscale realization theory has focused on
building tree models which match the covariance of a given process of
interest. In this research, we construct these models based solely on
realizations of the process, with no assumed knowledge of the
covariance. The most straightforward (but perhaps naive) approach to
this problem is to first estimate the covariance of the process from
sample paths and then use canonical correlations or related techniques
to build a model. However, in large-scale problems, such as the
ocean, this covariance is monstrously high-dimensional and therefore
unwieldy due to memory constraints. As a result, the essential
question which we must address is the following: how can we
efficiently update a tree model given a new sample path of a process?
Our approach to this problem is to use gradient descent to minimize an
appropriate cost function, which emphasizes the properties of the tree
model that we seek to exploit. The redeeming property of tree models
is, in fact, the Markov property, which allows an efficient estimation
algorithm. To build models with this property, we use a previously
proposed cost function that provides a measure of Markovianity. We
also introduce an information theoretic measure of Markovianity which
may ultimately lead to a "richer" set of tree models.
Master's Thesis: Wavelet Denoising Techniques with Applications to High-Resolution Radar
The classical estimation problem, that of estimating an unknown signal
in additive noise, has recently been revisited by researchers.
Wavelets and wavelet packets can be attributed to the resurgence of
interest in this area. One of the most significant properties of
wavelets, which we exploit, is their ability to represent signals in a
given smoothness class with very few large magnitude coefficients. In
this research, we find an ``optimal'' representation of a given signal
in a wavelet packet tree, such that removing noisy coefficients at a
given threshold improves the signal quality and minimizes the error in
reconstructing the signal.
To apply these denoising techniques, we seek a methodology that will
extract significant features from high-resolution radar (HRR) returns
for the purpose of Automatic Target Recognition (ATR). HRR profiles
are one-dimensional radar returns that provide a ``fingerprint'' of a
target. Using returns from a particular target, we create a database
that contains signals representative of the target at different azimuth
and elevation angles, and the database is extended to include many
possible targets. The ATR problem then reduces to a database
search procedure in order to determine a target's identity and
On Denoising and Best Signal Representation -- IEEE Transactions on Information Theory, November 1999.
Dewey S. Tucker received the B.E.E. degree from
the Georgia Institute of Technology, Atlanta, Georgia,
in 1995 and the S.M. degree in Electrical Engineering at M.I.T. in 1997.
He is pursuing a Ph.D. in Electrical Engineering at
M.I.T. He he has been working in
the Stochastic Systems Group, a part of the Laboratory for Information and Decision
Systems, since 1996. His research interest is in large-scale statistical modeling.