Journal ArticleDOI
Reconstruction of the support function for inclusion from boundary measurements
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In this article, a Dirichlet to Neumann map is used for the reconstruction of the support function for unknown inclusion in the Helmholtz equation, without the unique continuation property or Runge approximation property.Abstract:
Abstract - First we give a formula (procedure) for the reconstruction of the support function for unknown inclusion by means of the Dirichlet to Neumann map. In the procedure we never make use of the unique continuation property or the Runge approximation property of the governing equation. Second we apply the method to a similar problem for the Helmholtz equation.read more
Citations
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Journal ArticleDOI
A survey on sampling and probe methods for inverse problems
TL;DR: A survey of sampling and probe methods for the solution of inverse acoustic and electromagnetic scattering problems can be found in this paper, where the main ideas, approaches and convergence results of the methods are presented.
Journal ArticleDOI
Numerical implementation of two noniterative methods for locating inclusions by impedance tomography
Martin Brühl,Martin Hanke +1 more
TL;DR: In this paper, theoretical foundations have been developed for new techniques to localize inclusions from impedance tomography data, and these theoretical results lead quite naturally to noniterative numerical reconstruction algorithms.
Journal ArticleDOI
Explicit characterization of inclusions in electrical impedance tomography
TL;DR: It is shown that this procedure is conceptually similar to a recent method proposed by Kirsch in inverse scattering theory and holds true if and only if the dipole singularity lies inside the inhomogeneity.
Journal ArticleDOI
Monotonicity-based shape reconstruction in electrical impedance tomography ∗
Bastian Harrach,Marcel Ullrich +1 more
TL;DR: A converse of this simple monotonicity relation is presented and used to solve the shape reconstruction problem in EIT and find the outer shape of a region where the conductivity differs from a known background conductivity.
Journal ArticleDOI
Numerical method for finding the convex hull of an inclusion in conductivity from boundary measurements
Masaru Ikehata,Samuli Siltanen +1 more
TL;DR: In this article, the authors considered the 2D inverse conductivity problem for conductivities of the form γ = 1 + χDh defined in a bounded domain Ω⊂2 with C∞ boundary ∂Ω.
References
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Journal ArticleDOI
A global uniqueness theorem for an inverse boundary value problem
John Sylvester,Gunther Uhlmann +1 more
TL;DR: In this paper, the single smooth coefficient of the elliptic operator LY = v yv can be determined from knowledge of its Dirichlet integrals for arbitrary boundary values on a fixed region 2 C R', n? 3.
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Global uniqueness for a two-dimensional inverse boundary value problem
TL;DR: In this article, it was shown that the coefficient -y(x) of the elliptic equation Vie (QyVu) = 0 in a two-dimensional domain is uniquely determined by the corresponding Dirichlet-to-Neumann map on the boundary.
Journal ArticleDOI
Reconstructions from boundary measurements
TL;DR: In this paper, the authors define la forme quadratique Qγ sur H 1/2 (∂Ω) par Qγ(f)=∫ Ω γ(x)|⊇u (x)| 2 dx ou u∈H 1 (Ω), est la solution unique a Lγu=0 dans Ω, u| ∂ Ω =f.
Journal ArticleDOI
Determining conductivity by boundary measurements
Robert V. Kohn,Michael Vogelius +1 more
TL;DR: In this article, Calderon poses the question: "Is it possible to determine the conductivite thermique of an object by means of mesures statiques de la temperature and du flux de chaleur a la limite?"
Journal ArticleDOI
A uniqueness theorem for an inverse boundary value problem in electrical prospection
John Sylvester,Gunther Uhlmann +1 more
TL;DR: In this article, it was shown that a near constant conductivity of a two-dimensional body can be uniquely determined by steady state direct current measurements at the boundary of the body.
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