Tuesday, March 4, 2008
Mathematical Sciences Colloquium
Speaker: Erkki Somersalo (Helsinki University of Technology) "Hypermodels and Qualitative Information in Imaging"

In imaging applications, the typical problem is to reconstruct or recover an image based on incomplete, noisy and indirect information. The problem has all the typical characteristics of ill-posed inverse problems, such as non-uniqueness of the solution and high sensitivity to noise. To obtain a reasonable solution, the data have to be augmented by complementary information that is imported into the reconstruction algorithm either by classical regularization or recasting the problem in a statistical framework. Since often the complementary information is qualitative, it needs to be translated into a quantitative form before it can be used in the deterministic approach. In the Bayesian approach presented in this presentation, we show how hierarchical models provide a flexible framework for interpreting qualitative prior information, leading to effective numerical algorithms. Moreover, the approach allows the estimation of the credibility of the estimates, a feature that is particularly important in many medical imaging applications.

Prior to our colloquium, there will be an IPRPI reception from 3-4 on the fourth floor of Amos Eaton. Poster display by IPRPI advised grad student/postdocs will be included.