Hostname: page-component-7c8c6479df-xxrs7 Total loading time: 0 Render date: 2024-03-27T06:51:42.994Z Has data issue: false hasContentIssue false

A survey on level set methods for inverse problems and optimal design

Published online by Cambridge University Press:  03 June 2005

MARTIN BURGER
Affiliation:
Industrial Mathematics Institute, Johannes Kepler Universität, Altenbergerstr. 69, 4040 Linz, Austria email :martin.burger@jku.at
STANLEY J. OSHER
Affiliation:
Department of Mathematics, UCLA, 520 Portola Plaza, Los Angeles, CA 90095, USA email: sjo@math.ucla.edu

Abstract

The aim of this paper is to provide a survey on the recent development in level set methods in inverse problems and optimal design. We give introductions on the general features of such problems involving geometries and on the general framework of the level set method. In subsequent parts we discuss shape sensitivity analysis and its relation to level set methods, various approaches on constructing optimization algorithms based on the level set approach, and special tools needed for the application of level set based optimization methods to ill-posed problems. Furthermore, we provide a review on numerical methods important in this context, and give an overview of applications treated with level set methods. Finally, we provide a discussion of the most challenging and interesting open problems in this field, that might be of interest for scientists who plan to start future research in this field.

Type
Research Article
Copyright
2005 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)