Computational Inverse Problems

What it is about

You will learn mathematical and numerical methods for solving mainly linear inverse problems. In the end you will know the theory (ill-posedness, regularization, SVD, generalized Tikhonov) and common numerical procedures (direct and iterative regularization) as well as criteria for stability, convergence and stopping.

What you will be able to do

• Understand properties and theory of inverse problems
• Describe the degree of ill-posedness
• Assess optimal accuracy estimates
• Apply analytical regularization tools (filters, generalized inverse, SVD, Tikhonov)
• Apply important numerical algorithms (truncated SVD, Tikhonov, Landweber, gradient methods)
• Select parameter choices and stopping criteria for regularization techniques
• Apply algorithms for typical applications (e.g., medical image analysis)

What the module consists of

• LectureConveying theory and demonstrative examples
• Exercise / practice sessionsDeepening through problem sheets and solutions, self-check

Teaching method

• Lecture with discussionPresentation of the content and exchange with students
• Integrated practice sessions with exercise sheetsDeepening understanding and checking learning progress