AN ANISOTROPIC INVERSE BOUNDARY-VALUE PROBLEM

We consider the impedance tomography problem for anisotropic conductivities. Given a bounded region Ω in space, a diffeomorphism Ψ from Ω to itself which restricts to the identity on ∂ Ω, and a conductivity γ on Ω, it is easy to construct a new conductivity Ψ*γ which will produce the same voltage and current measurements on ∂ Ω. We prove the converse in two dimensions (i.e., if γ1 and γ2 produce the same boundary measurements, then γ1, = Ψ*γ2 for an appropriate Ψ) for conductivities which are near a constant. Copyright © 1990 Wiley Periodicals, Inc., A Wiley Company