Jump to ContentJump to Main Navigation
Show Summary Details
In This Section

Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


IMPACT FACTOR 2016: 0.783
5-year IMPACT FACTOR: 0.792

CiteScore 2016: 0.80

SCImago Journal Rank (SJR) 2015: 0.583
Source Normalized Impact per Paper (SNIP) 2015: 1.106

Mathematical Citation Quotient (MCQ) 2015: 0.43

Online
ISSN
1569-3945
See all formats and pricing
In This Section
Volume 17, Issue 8 (Jan 2009)

Issues

A shape calculus analysis for tracking type formulations in electrical impedance tomography

K. Eppler
Published Online: 2009-11-25 | DOI: https://doi.org/10.1515/JIIP.2009.043

Abstract

In the paper [Eppler and Harbrecht, Control & Cybernetics 34: 203–225, 2005], the authors investigated the identification of an obstacle or void of perfectly conducting material in a two-dimensional domain by measurements of voltage and currents at the boundary. In particular, the reformulation of the given nonlinear identification problem was considered as a shape optimization problem using the Kohn and Vogelius criterion. The compactness of the complete shape Hessian at the optimal inclusion was proven, verifying strictly the ill-posedness of the identification problem. The aim of the paper is to present a similar analysis for the related least square tracking formulations. It turns out that the two-norm-discrepancy is of the same principal nature as for the Kohn and Vogelius objective. As a byproduct, the necessary first order optimality condition are shown to be satisfied if and only if the data are perfectly matching. Finally, we comment on possible consequences of the two-norm-discrepancy for the regularization issue.

Key words.: Electrical impedance tomography; shape calculus; boundary integral equations; ill-posed problems; two norm discrepancy

About the article

Received: 2008-11-11

Published Online: 2009-11-25

Published in Print: 2009-11-01



Citation Information: Journal of Inverse and Ill-posed Problems, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/JIIP.2009.043. Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Alexey Chernov, Duong Pham, and Thanh Tran
Computers & Mathematics with Applications, 2015

Comments (0)

Please log in or register to comment.
Log in