Title

ON A CALDERON PROBLEM IN FREQUENCY DIFFERENTIAL ELECTRICAL IMPEDANCE TOMOGRAPHY

Authors

Authors

S. Kim;A. Tamasan

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

SIAM J. Math. Anal.

Keywords

Calderon problem; frequency differential electrical impedance; tomography; complex geometrical optics; BOUNDARY-VALUE PROBLEM; GLOBAL UNIQUENESS; FEASIBILITY; Mathematics, Applied

Abstract

Recent research in electrical impedance tomography produced images of biological tissue from frequency differential boundary voltages and corresponding currents. Physically one is to recover the electrical conductivity sigma and permittivity c from the frequency differential boundary data. Let gamma = sigma+iota omega is an element of denote the complex admittivity, Lambda(gamma) be the corresponding Dirichlet-to-Neumann map, and d Lambda(gamma)/d omega|omega=0 be its frequency differential at omega = 0. If sigma is an element of C-1,C-1 ((Omega) over bar) is constant near the boundary and is an element of is an element of C-0(1,1) (Omega), we show that d Lambda(gamma)/d omega|omega=0 uniquely determines del center dot (del is an element of - is an element of del ln sigma)/sigma inside Omega. In addition, if Lambda(gamma)|(omega=0) is also known, then is an element of and sigma can be reconstructed inside. The method of proof uses the complex geometrical optics solutions.

Journal Title

Siam Journal on Mathematical Analysis

Volume

45

Issue/Number

5

Publication Date

1-1-2013

Document Type

Article

Language

English

First Page

2700

Last Page

2709

WOS Identifier

WOS:000326383600006

ISSN

0036-1410

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