Bregman distances in inverse problems and partial differential equations

Article in Edited Volumes


Publication Details

Author(s): Burger M
Editor(s): J.Hiriard-Urrurty, A.Korytowski, H.Maurer, M.Szymkat
Title edited volumes: Advances in Mathematical
Modeling, Optimization, and Optimal Control

Publisher: Springer International Publishing
Publication year: 2016
Title of series: Springer Optimization and Its Applications
Pages range: 3-33
ISSN: 1931-6828


Abstract

The aim of this paper is to provide an overview of recent development related to Bregman distances outside its native areas of optimization and statistics. We discuss approaches in inverse problems and image processing based on Bregman distances, which have evolved to a standard tool in these fields in the last decade. Moreover, we discuss related issues in the analysis and numerical analysis of nonlinear partial differential equations with a variational structure. For such problems Bregman distances appear to be of similar importance, but are currently used only in a quite hidden fashion. We try to work out explicitly the aspects related to Bregman distances, which also lead to novel mathematical questions and may also stimulate further research in these areas.


External institutions with authors

Westfälische Wilhelms-Universität (WWU) Münster


How to cite

APA:
Burger, M. (2016). Bregman distances in inverse problems and partial differential equations. In J.Hiriard-Urrurty, A.Korytowski, H.Maurer, M.Szymkat (Eds.), Advances in Mathematical Modeling, Optimization, and Optimal Control. (pp. 3-33). Springer International Publishing.

MLA:
Burger, Martin. "Bregman distances in inverse problems and partial differential equations." Advances in Mathematical Modeling, Optimization, and Optimal Control. Ed. J.Hiriard-Urrurty, A.Korytowski, H.Maurer, M.Szymkat, Springer International Publishing, 2016. 3-33.

BibTeX: 

Last updated on 2018-30-11 at 14:38