Title

Conductivity Imaging With A Single Measurement Of Boundary And Interior Data

Abstract

We consider the problem of imaging the conductivity from knowledge of one current and corresponding voltage on a part of the boundary of an inhomogeneous isotropic object and of the magnitude |J(x)| of the current density inside. The internal data are obtained from magnetic resonance measurements. The problem is reduced to a boundary value problem with partial data for the equation ∇ |J(x)||∇u|-1∇u = 0. We show that equipotential surfaces are minimal surfaces in the conformal metric |J|2/(n-1)I. In two dimensions, we solve the Cauchy problem with partial data and show that the conductivity is uniquely determined in the region spanned by the characteristics originating from the part of the boundary where measurements are available. We formulate sufficient conditions on the Dirichlet data to guarantee the unique recovery of the conductivity throughout the domain. The proof of uniqueness is constructive and yields an efficient algorithm for conductivity imaging. The computational feasibility of this algorithm is demonstrated in numerical experiments. © 2007 IOP Publishing Ltd.

Publication Date

12-1-2007

Publication Title

Inverse Problems

Volume

23

Issue

6

Number of Pages

2551-2563

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1088/0266-5611/23/6/017

Socpus ID

36749073048 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/36749073048

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