Authors

A. Moradifam; A. Nachman;A. Tamasan

Comments

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Abbreviated Journal Title

SIAM J. Math. Anal.

Keywords

conductivity imaging; current density impedance imaging; minimal; surfaces; 1-Laplacian; ELECTRICAL-IMPEDANCE TOMOGRAPHY; J-SUBSTITUTION ALGORITHM; B-Z; ALGORITHM; MAGNETIC-RESONANCE; CURRENT-DENSITY; RECONSTRUCTION; MREIT; CONVERGENCE; UNIQUENESS; EQUATION; Mathematics, Applied

Abstract

We consider the problem of recovering an isotropic conductivity outside some perfectly conducting inclusions or insulating inclusions from the interior measurement of the magnitude of one current density field vertical bar J vertical bar. We show that the conductivity outside the inclusions and the shape and position of the inclusions are uniquely determined (except in an exceptional case) by the magnitude of the current generated by imposing a given boundary voltage. Our results show that even when the minimizer of the least gradient problem min integral(Omega) a|del u| with u vertical bar(partial derivative Omega) = f exhibits flat regions (i.e., regions with del u = 0) it can be identified as the voltage potential of a conductivity problem with perfectly conducting inclusions.

Journal Title

Siam Journal on Mathematical Analysis

Volume

44

Issue/Number

6

Publication Date

1-1-2012

Document Type

Article

Language

English

First Page

3969

Last Page

3990

WOS Identifier

WOS:000312727800011

ISSN

0036-1410

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