DSP seminar: October 16, 1997

	Bayesian Models in Tomography and Imaging

	Charles A. Bouman
	Purdue University
	School of Electrical and Computer Engineering
	West Lafayette IN 47907

Many problems in image processing require the recovery of an unknown image
from noisy or incomplete information. For example, tomographic
reconstruction requires that an unknown image (or volume) be estimated from
a set of projection measurements. Often, these measurements may be noisy or
incomplete, so the exact solution can not be obtained through a simple
inverse operation. For such ill-posed inverse problems, it is very useful
to incorporate an image model into the inversion process since the model
can capture essential characteristics such as smooth regions and edges in
images. In particular, Bayesian statistical techniques form an elegant
framework for incorporating such prior knowledge about image behavior
through an assumed prior image distribution.

This talk focuses on some key aspects of good prior image models and
illustrates their value in the context of two applications: tomography and
segmentation. In particular, we argue that a good model should be:

	1) Robust and/or adaptable to image behavior
	2) Able to model both global and local image characteristics
	3) Computationally tractable

We first briefly review methods for applying the Bayesian estimation
framework to tomographic reconstruction problems and show how Markov random
fields (MRF) can be used to simply model image cross-sections. We discuss
how proper choice of the MRF model can improve robustness, and how the
model can be automatically adapted through the use of parameter estimation
methods based on the expectation maximization EM algorithm. We next
introduce a class of prior models based on a multiscale structure which are
better suited to modeling more global image characteristics, and we present
examples of their use in both tomography and segmentation applications.