Methods for Inverse Problems

What it is about

You will learn mathematical foundations and numerical methods for solving inverse problems. The focus is on regularization techniques for linear and nonlinear problems as well as iterative solution methods (gradient-, Newton-, and Kaczmarz-type) and practical aspects such as adaptive discretization in PDE-based reconstruction tasks.

What you will be able to do

• Knowledge of regularization theory for linear inverse problems
• Understanding of Tikhonov regularization for nonlinear problems
• Proficiency with iterative solving procedures (gradient- and Newton-type)
• Application and extension to Kaczmarz variants and higher-order methods
• Use of all-at-once formulations and adaptive discretization in PDE reconstructions
• Ability to theoretically analyze and implement the methods

What the module consists of

• LectureConveying the theoretical foundations and demonstrative examples; discussion with students

Teaching method

• Lecture with examplesfor introduction to theory and practice
• Discussionfor deepening and motivation of own analyses as well as for self-study preparation