## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Module MAT-70-13-M-7

## Module Identification

Module Number Module Name CP (Effort)
MAT-70-13-M-7 Inverse Problems 9.0 CP (270 h)

## Basedata

CP, Effort 9.0 CP = 270 h 1 Sem. irreg. [7] Master (Advanced) [EN] English Steidl, Gabriele, Prof. Dr. (PROF | DEPT: MAT) Steidl, Gabriele, Prof. Dr. (PROF | DEPT: MAT) [MAT-SPAS] Analysis and Stochastics [MAT-88.105-SG] M.Sc. Mathematics [NORM] Active

## Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-70-13-K-7
Inverse Problems
P 84 h 186 h - - PL1 9.0 irreg.
• About [MAT-70-13-K-7]: Title: "Inverse Problems"; Presence-Time: 84 h; Self-Study: 186 h

## Examination achievement PL1

• Form of examination: oral examination (20-30 Min.)
• Examination Frequency: irregular (by arrangement)
• Examination number: 86260 ("Inverse Problems")

## Contents

• introductory examples,
• ill-posed operator equations,
• regularisation methods (singular value decomposition, Tikhonov regularization, iterative methods, multi-resolution techniques).

## Competencies / intended learning achievements

Upon successful completion of this module, the students have gained mathematical skills in the area of inverse problems (to be able to get information about inaccessible data from measurable and/or observable effects). They understand and master stabilisation and regularisation techniques and they are able to justify the theory by experiments (clarification by means of examples). They understand the mathematical background required for the algorithms and can critically assess the possibilities and limitations of their use. They understand the proofs presented in the lecture and are able to reproduce and explain them. In particular, they can critically assess, what conditions are necessary for the validity of the statements.

By solving the given exercise problems, they have gained a precise and independent handling of the terms, propositions and methods of the lecture. In addition, they have learnt to apply the methods to new problems, analyze them and develop solution strategies independently or by team work.

## Literature

• D. Colton, R. Kress: Inverse Acoustic and Electromagnetic Scattering Theory,
• A. Kirsch: An Introduction to the Mathematical Theory of Inverse Problems,
• A. Louis: Inverse und schlecht gestellte Probleme,
• A. Rieder: Keine Probleme mit inversen Problemen.

None

## References to Module / Module Number [MAT-70-13-M-7]

Module-Pool Name
[MAT-65-MPOOL-7] Specialisation Image Processing and Data Analysis (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)