Only for ETH D-MATH doctoral students and for doctoral students from the Institute of Mathematics at UZH. The latter need to send an email to Jessica Bolsinger (info@zgsm.ch) with the course number. The email should have the subject „Graduate course registration (ETH)“.
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.
Lernziel
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.
Inhalt
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.
Skript
The lecture notes will be made available during the semester.
Literatur
Engl, H. W., Hanke, M., & Neubauer, A. (1996). Regularization of inverse problems (Vol. 375). Springer Science & Business Media.
Voraussetzungen / Besonderes
Analysis, linear algebra, numerical analysis, ideal but not necessary: functional analysis
Kompetenzen
Fachspezifische Kompetenzen
Konzepte und Theorien
geprüft
Verfahren und Technologien
geprüft
Methodenspezifische Kompetenzen
Analytische Kompetenzen
geprüft
Problemlösung
geprüft
Persönliche Kompetenzen
Kreatives Denken
gefördert
Kritisches Denken
geprüft
Leistungskontrolle
Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)
Leistungskontrolle als Semesterkurs