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Probing for electrical inclusions with complex spherical waves
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DOI：10.1002/cpa.20194.png)
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Abstract
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Let a physical body Omega in R-2 or R-3 be given. Assume that the electric conductivity distribution inside Omega consists of conductive inclusions in a known smooth background. Further, assume that a subset Gamma subset of partial derivative Omega is available for boundary measurements. It is proved using hyperbolic geometry that certain information about the location of the inclusions can be exactly recovered from static electric measurements on Gamma. More precisely: given a ball B with center outside the convex hull of Omega and satisfying ((B) over bar boolean AND partial derivative Omega ) subset of Gamma, boundary measurements on Gamma with explicitly given Dirichlet data are enough to determine whether B intersects the inclusion. An approximate detection algorithm is introduced based on the theory. Numerical experiments in dimension two with simulated noisy data suggest that the algorithm finds the inclusion-free domain near Gamma and is robust against measurement noise. (c) 2006 Wiley Periodicals, Inc.
Keywords:
INVERSE CONDUCTIVITY PROBLEM
BOUNDARY-VALUE PROBLEM
IMPEDANCE TOMOGRAPHY
RESISTANCE TOMOGRAPHY
GLOBAL UNIQUENESS
NUMERICAL-METHOD
NEUMANN MAP
CONVEX-HULL
CAUCHY DATA
RECONSTRUCTION
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