Modern regularization methods for inverse problems

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autorinnen und Autoren: Burger M
Zeitschrift: Acta Numerica
Verlag: CAMBRIDGE UNIV PRESS
Jahr der Veröffentlichung: 2018
Band: 27
Seitenbereich: 1-111
ISSN: 0962-4929


Abstract

Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and allow a robust approximation of ill-posed (pseudo-) inverses. In the last two decades interest has shifted from linear to nonlinear regularization methods, even for linear inverse problems. The aim of this paper is to provide a reasonably comprehensive overview of this shift towards modern nonlinear regularization methods, including their analysis, applications and issues for future research.In particular we will discuss variational methods and techniques derived from them, since they have attracted much recent interest and link to other fields, such as image processing and compressed sensing. We further point to developments related to statistical inverse problems, multiscale decompositions and learning theory.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Burger, Martin Prof. Dr.
Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Zuletzt aktualisiert 2019-15-02 um 08:08