CONDUCTIVITY IMAGING FROM ONE INTERIOR MEASUREMENT IN THE PRESENCE OF PERFECTLY CONDUCTING AND INSULATING INCLUSIONS
Abbreviated Journal Title
SIAM J. Math. Anal.
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
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.
Siam Journal on Mathematical Analysis
"CONDUCTIVITY IMAGING FROM ONE INTERIOR MEASUREMENT IN THE PRESENCE OF PERFECTLY CONDUCTING AND INSULATING INCLUSIONS" (2012). Faculty Bibliography 2010s. 3045.