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Mathematics and Statistics Colloquium
Date/Time/Room:
Friday (9/21/2007) at 2:30pm in 304 Pickard Hall "Multilevel Methods for IllPosed Problems"Abstract: Multilevel methods are popular for the solution of wellposed problems, such as certain boundary value problems for partial differential equations and Fredholm integral equations of the second kind. However, little is known about the behavior of multilevel methods when applied to the solution of linear illposed problems, such as Fredholm integral equations of the first kind, with a righthand side that is contaminated by error. We discuss properties of cascadic multilevel methods with a conjugate gradienttype method as basic iterative scheme. In particular, we consider applications to image deblurring and denoising using edgepreserving prolongation operators based on partial differential equations defined by PeronaMalik and total variationtype models. The talk presents joint work with Serena Morigi, Fiorella Sgallari, and Andriy Shyshkov.

