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401-4652-23L 4 Credits DR , MSC D-MATH

Inverse Problems

Lecturers & Examiners: Dr. Rima Alaifari
VVZ CR n/a

Last Updated: 2026-02-05 16:29:40

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
  • Wed 10:15-12:00 (HG G 3)
2 h weekly

Offered In