TITLE
Bayesian Inference via the Variational Approximation for Inverse Problems in Image Processing
ABSTRACT
Inverse imaging problems are frequently found in many modern technological applications.
Examples of such technological applications are: visual communications, and medical imaging.
The main attribute of inverse imaging problems is that the observed data do not specify uniquely
the source image from which they were obtained. Thus, apart from the observations one has to use
prior knowledge to uniquely estimate the source image.
Bayesian Inference is a methodology according to which prior knowledge is introduced in a very
natural manner in estimation problems, as the one above, through the use of a prior. This prior
captures the prior knowledge about the source that we desire to estimate. The Variational
approximation is a recent methodology for Bayesian Inference which has a number of advantages.
First, it provides estimates of the posterior for complex models where the marginalization of
the hidden variables is not possible. Second, it is very fast, unlike time consuming Markov
Chain Monte Carlo approaches, since it is deterministic in nature.
In this talk we will present a family of new image priors that model local salient features of
images. Furthermore, we will demonstrate how the Variational approximation can be used to bypass
the difficulties of Bayesian Inference with such priors in a number of image processing problems.
We shall also show numerical experiments that demonstrate the advantages of the proposed methodology.
SPEAKER BIO
Nikolas P. Galatsanos received the Diploma of Electrical Engineering from the National Technical
University of Athens Greece in 1982. He received the MSEE and Ph. D. degrees from the Electrical
and Computer Engineering Department of the University of Wisconsin-Madison in 1984 and 1989,
respectively. He was on the faculty of the Electrical and Computer Engineering Department of the
Illinois Institute of Technology, Chicago, Illinois and the Computer Science Department of the
University of Ioannina, Ioannina, Greece during the periods 1989-2002 and 2002-2007, respectively.
Currently, he is on the faculty of the Electrical and Computer Engineering Department of the University
of Patras, Patras, Greece. His research interests center around Bayesian methods for image processing
and statistical learning problems. He has served as an Associate Editor for the IEEE Transactions on
Image Processing and the IEEE Signal Processing Magazine. Dr. Galatsanos has coedited a book titled:
Image Recovery Techniques for Image and Video Compression and Transmission, Kluwer Academic, October 1998.