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Lecture: 03-M-SP-1 Inverse Problems - Details

Lecture: 03-M-SP-1 Inverse Problems - Details

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General information

Course name Lecture: 03-M-SP-1 Inverse Problems
Subtitle
Course number 03-M-SP-1
Semester SoSe 2025
Current number of participants 22
Home institute Mathematik
Courses type Lecture in category Teaching
Next date Thursday, 19.06.2025 12:00 - 14:00, Room: MZH 4140
Type/Form Lecture including Exercises
Englischsprachige Veranstaltung Ja
ECTS points 9

Rooms and times

MZH 4140
Thursday: 12:00 - 14:00, weekly (9x)
Friday: 12:00 - 14:00, weekly (12x)
Friday: 14:00 - 16:00, weekly (11x)
MZH 2340
Thursday: 12:00 - 14:00, weekly (3x)
Friday: 12:00 - 14:00, weekly (1x)
Friday: 14:00 - 16:00, weekly (2x)

Module assignments

Comment/Description

Inverse problems are problems where one would like to find an unknown cause for which one can only measure observed effects. This situation occurs, for example, if one can only make indirect measurements of the quantity of interest. Two simple examples: \begin{itemize} \item We measure the position of an object, but would like to know the speed. \item In tomography we measure several projections (X-ray images) of an object, but would like to know the absorption spectrum of said object. \end{itemize} Inverse problems usually suffer from ill-posedness: Solutions may not be unique, they may not exist (for example due to measurement noise), and, most drastically, their solution is unstable in the sense that it does not depend continuously on the data. We will analyze the phenomenon on ill-posedness for linear inverse problems (modeled as linear and continuous maps between Hilbert spaces) to understand the reason for instability. A central goal of the course is to establish the notion of regularization of ill-posed problems (which roughly means the approximate solution by stable methods) and to derive and analyze regularization methods such as Tikhonov regularization, or the Landweber method with early stopping. We will also treat the numerical solution of inverse problems in the lecture and the exercises.

Registration mode

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