401-4652-23L  Inverse Problems

SemesterFrühjahrssemester 2023
DozierendeR. Alaifari
Periodizitäteinmalige Veranstaltung
LehrspracheEnglisch


KurzbeschreibungInverse 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.
LernzielThe 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.
InhaltLinear 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.
SkriptThe lecture notes will be made available during the semester.
LiteraturEngl, H. W., Hanke, M., & Neubauer, A. (1996). Regularization of inverse problems (Vol. 375). Springer Science & Business Media.
Voraussetzungen / BesonderesAnalysis, linear algebra, numerical analysis, ideal but not necessary: functional analysis
KompetenzenKompetenzen
Fachspezifische KompetenzenKonzepte und Theoriengeprüft
Verfahren und Technologiengeprüft
Methodenspezifische KompetenzenAnalytische Kompetenzengeprüft
Problemlösunggeprüft
Persönliche KompetenzenKreatives Denkengefördert
Kritisches Denkengeprüft