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Lothar Reichel (Kent State University, OH, USA)
| Speaker: |
Lothar Reichel (Kent State
University, OH, USA)
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| Date: |
Wednesday July 8, 2009
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| Title: |
Multilevel Methods
for Ill-Posed Problems
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Abstract
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Multilevel methods are popular
for the solution of well-posed 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
ill-posed problems, such as Fredholm integral equations of the first
kind, with a right-hand side that is contaminated by error. We discuss
properties of cascadic multilevel methods with a conjugate
gradient-type method as basic iterative scheme. In particular, we
consider applications to image deblurring, denoising, and segmentation.
The multilevel methods blend linear algebra and partial differential
equation techniques. Deblurring and denoising are achieved by using
edge-preserving prolongation operators based on partial differential
equations defined by Perona-Malik models.
The talk presents joint work with Serena Morigi, Fiorella Sgallari, and
Andriy Shyshkov.
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