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
DOI Link
Language
English
First Page
3969
Last Page
3990
WOS Identifier
ISSN
0036-1410
Recommended Citation
Moradifam, Amir; Nachman, Adrian; and Tamasan, Alexandru, "Conductivity Imaging from One Interior Measurement In The Presence Of Perfectly Conducting And Insulating Inclusions" (2012). Faculty Bibliography 2010s. 3045.
https://stars.library.ucf.edu/facultybib2010/3045
Comments
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