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   -> Volume 2, Issue 9

PhD thesis abstract
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Mark Luettgen, MIT

PostPosted: Fri Nov 29, 2002 3:31 pm    
Subject: PhD thesis abstract
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PhD thesis abstract

Author: Mark R. Luettgen
Advisor: Prof. Alan S. Willsky
Title: Image Processing with Multiscale Stochastic Models
Institution: Massachusetts Institute of Technology

Copies: This thesis can be obtained by writing to:

MIT Laboratory for Information and Decision Systems
Publications Office
Room 35-311
77 Massachusetts Ave.
Cambridge, MA 02139

or via anonymous ftp from:
machine name:, directory: pub/ssg/papers

In this thesis, we develop image processing algorithms and
applications for a particular class of multiscale stochastic models.
First, we provide background on the model class, including a
discussion of its relationship to wavelet transforms and the details
of a two-sweep algorithm for estimation. A multiscale model for the
error process associated with this algorithm is derived. Next, we
illustrate how the multiscale models can be used in the context of
regularizing ill-posed inverse problems and demonstrate the
substantial computational savings that such an approach offers.
Several novel features of the approach are developed including a
technique for choosing the optimal resolution at which to recover the
object of interest. Next, we show that this class of models contains
other widely used classes of statistical models including 1-D Markov
processes and 2-D Markov random fields, and we propose a class of
multiscale models for approximately representing Gaussian Markov
random fields. These results, coupled with those illustrating the
computational efficiencies that the multiscale models lead to, suggest
that the multiscale framework is a powerful paradigm for image
processing both because of the efficient algorithms it admits and
because of the rich class of phenomena it can be used to describe.
This motivates us in the final section of this thesis to pursue
further algorithmic development for the multiscale models. In
particular, we develop an efficient likelihood calculation algorithm
for multiscale models and demonstrate an application of the algorithm
in the area of texture discrimination. The thesis concludes with a
review of our main results and with a discussion of a few of the many
open problems and promising directions for further research and
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