Dewey S. Tucker

Room 35-427

253-7220


Research Statements


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 spatial orientation.


Publication:

On Denoising and Best Signal Representation -- IEEE Transactions on Information Theory, November 1999.


Brief Biography

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.


Email: dtucker@mit.edu
Links: SSG, LIDS