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Copyright © 2011 Claremont Center for the Mathematical Sciences

When

Start: 02/15/2008 - 1:30pm

End : 02/15/2008 - 2:30pm

End : 02/15/2008 - 2:30pm

Category

Applied Math Seminar

Speaker

Prof. Daniela Calvetti (Case Western Reserve University)

Abstract

We consider the problem of restoring an image from a noisy blurred

copy, with the additional qualitative information that the

image contains sharp discontinuities of unknown size and location.

The flexibility of the Bayesian imaging framework is

particularly convenient in the presence of such qualitative, rather

than quantitative, information. By using a non-stationary Markov

model with the variance of the innovation process also unknown, it

is possible to take advantage of the qualitative prior information,

and Bayesian techniques can be applied to estimate simultaneously

the unknown and the prior variance. Here we present a unified

approach to Bayesian signal and imaging, and show that with rather

standard choices of hyperpriors we obtain some classical

regularization methods as special cases. The application of Bayesian

hyperprior models to imaging applications requires a careful

organization of the computations to overcome the challenges coming

from the high dimensionality. We explain how the computation of

MAP estimates within the proposed Bayesian framework can be made

very efficiency by a judicious use of Krylov iterative methods and

priorconditioners. The Bayesian approach, unlike deterministic

methods which produce a single solution image, provides a

very natural way to assess the reliability of single image estimates

by a Markov Chain Monte Carlo (MCMC) based analysis of the

posterior. Computed examples illustrate the different features and

the computational properties of the Bayesian hypermodel approach to

imaging.

Where

Math South, 710 N. College Ave
On map http://www.cgu.edu/pages/3233.asp, see location 16