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Inverse Problems
Last Updated: 2026-02-05 16:22:14
Abstract
Inverse problems arise in many applications in science & engineering. Typically, a physical model describes a forward problem and the task is to reconstruct from measurements, i.e. to perform inversion. In ill-posed problems, these inversions are troublesome as the inverse lacks e.g. stability. Regularization theory studies the controlled extraction of information from such systems.
Objective
The goal of this course is to give an understanding of ill-posedness and how it arises and to introduce the theory of regularization, which gives a mathematical framework to handle these delicate systems.
Content
Linear inverse problems, compact operators and singular value decompositions, regularization of linear inverse problems, regularization penalties, regularization parameters and parameter choice rules, iterative regularization schemes and stopping criteria, non-linear inverse problems.
Resources
Lecture Notes
The lecture notes will be made available during the semester.
Literature
Engl, H. W., Hanke, M., & Neubauer, A. (1996). Regularization of inverse problems (Vol. 375). Springer Science & Business Media.
General Information
- Language
- English
- Levels
- DR , MSC
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise | Inverse Problems |
|
2 h weekly |
Offered In
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Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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Signal Processing and Machine Learning (The core courses and specialization courses below are a selection for students who wish to specialize in the area of "Signal Processing and Machine Learning ", see . The individual study plan is subject to the tutor's approval.)
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Specialization Courses (These specialization courses are particularly recommended for the area of "Signal Processing and Machine Learning", but you are free to choose courses from any other field in agreement with your tutor. A minimum of 40 credits must be obtained from specialization courses during the MSc EEIT.)
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Major Courses (A total of 42 CP must be achieved form courses during the Master Program. The individual study plan is subject to the tutor's approval.)
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Doctorate Information Technology and Electrical Engineering (More Information at: )
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Subject Specialisation (A minimum of 12 ECTS credit points must be obtained during doctoral studies (also see other categories for details) The courses on offer below are but a small selection out of a much larger available number of courses. Please discuss your course selection with your PhD supervisor.)
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