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Bregman Distances in Inverse Problems and Partial Differential Equations

  • Martin BurgerEmail author
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 109)

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.

Keywords

Planck Equation Nonlinear Evolution Equation Optimal Transport Lyapunov Functional Convex Functional 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This work was partially supported by ERC via Grant EU FP 7 - ERC Consolidator Grant 615216 LifeInverse and by the German Science Foundation DFG via BU 2327/6-1 and EXC 1003 Cells in Motion Cluster of Excellence, Münster, Germany

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institut für Numerische und Angewandte MathematikWestfälische Wilhelms-Universität (WWU) Münster. Einsteinstr. 62MünsterGermany

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