Probing for electrical inclusions with complex spherical waves |
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| Authors: | Takanori Ide Hiroshi Isozaki Susumu Nakata Samuli Siltanen Gunther Uhlmann |
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| Institution: | 1. Tokyo Metropolitan University, Department of Mathematics, 1‐1 Minami‐Ohsawa, Hachioji‐shi, Japan;2. University of Tsukuba, Institute of Mathematics, 305‐8571 Tsukuba, Japan;3. Ritsumeikan University, College of Information Science and Engineering, 1‐1‐1 Noji‐Higashi, Kusatsu, 525‐8577 Shiga, Japan;4. Tampere University of Technology, Institute of Mathematics, P.O. Box 553, FI‐33101 Tampere, Finland;5. University of Washington, Department of Mathematics, Box 354350, Seattle, WA 98195‐4350 |
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| Abstract: | Let a physical body Ω in ?2 or ?3 be given. Assume that the electric conductivity distribution inside Ω consists of conductive inclusions in a known smooth background. Further, assume that a subset Γ ? ?Ω 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 Γ. More precisely: given a ball B with center outside the convex hull of Ω and satisfying (B? ∩ ?Ω) ? Γ, boundary measurements on Γ 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 Γ and is robust against measurement noise. © 2007 Wiley Periodicals, Inc. |
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