TIES6823 Iterative Regularization Methods for Inverse Problems (JSS29) (2 cr)
Study level:
Advanced studies
Grading scale:
Pass - fail
Language:
English
Responsible organisation:
Faculty of Information Technology
Curriculum periods:
2017-2018, 2018-2019, 2019-2020
Description
Content
This course deals with iterative methods for nonlinear ill-posed problems. After an introduction to linear regularization theory and a short excursion to Tikhonov regularization for nonlinear problems, we present gradient and Newton type methods as well as nonstandard iterative algorithms such as Kaczmarz, Halley, expectation maximization, and Bregman iterations. Our emphasis here is on convergence results in the sense of regularization where we intend to also sketch some of the proofs and show numerical results in order to provide insight on the regularizing mechanisms; if time permits, we will also give an outlook to all-at-once formulations and adaptive discretization.
Completion methods
Attendance and solving exercises.
Learning outcomes
After successful completion of this course, students will know methods and corresponding convergence results on modern regularization methods for inverse problems, in particular iterative reconstruction methods. They will understand these convergence results as well as their proofs and will be able to apply these methods.
Description of prerequisites
Course is aimed at PhD students and postdocs. Master students with good knowledge in functional analysis and PDEs could take part as well.
Completion methods
Method 1
Select all marked parts
Parts of the completion methods
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Unpublished assessment item