Monotonicity-based shape reconstruction in electrical impedance tomography ∗
Bastian Harrach,Marcel Ullrich +1 more
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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.Abstract:
Current-voltage measurements in electrical impedance tomography (EIT) can be partially ordered with respect to definiteness of the associated self-adjoint Neumann-to-Dirichlet operators. With this ordering, a pointwise larger conductivity leads to smaller current-voltage measurements, and smaller conductivities lead to larger measurements. We present a converse of this simple monotonicity relation and use it to solve the shape reconstruction (a.k.a. inclusion detection) problem in EIT. The outer shape of a region where the conductivity differs from a known background conductivity can be found by simply comparing the measurements to that of smaller or larger test regions.read more
Citations
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Journal ArticleDOI
Resolution Guarantees in Electrical Impedance Tomography
Bastian Harrach,Marcel Ullrich +1 more
TL;DR: In this article, it is shown that it is possible to give rigorous resolution guarantees in EIT even in the presence of systematic and random measurement errors, and a constructive criterion to decide whether a desired resolution can be achieved in a given measurement setup is derived.
Journal ArticleDOI
Recent Progress on the Factorization Method for Electrical Impedance Tomography
TL;DR: This work formulation of the Factorization Method for EIT with continuous data is presented and the method for general piecewise analytic conductivities is formulated and given short and self-contained proofs.
Journal ArticleDOI
Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography
Henrik Garde,Stratos Staboulis +1 more
TL;DR: In this paper, a monotonicity-based shape reconstruction scheme was proposed for electrical impedance tomography, which applies to approximative measurement models, and regularizes against noise and modelling error.
Posted Content
Monotonicity-based inversion of the fractional Schr\"odinger equation
Bastian Harrach,Yi-Hsuan Lin +1 more
TL;DR: In this article, if-and-only-if monotonicity relations between positive bounded potentials and their associated nonlocal Dirichlet-to-Neumann maps are provided.
Journal ArticleDOI
Resolution Guarantees in Electrical Impedance Tomography
Bastian Harrach,Marcel Ullrich +1 more
TL;DR: This work shows that it is principally possible to give rigorous resolution guarantees in EIT even in the presence of systematic and random measurement errors, and derives a constructive criterion to decide whether a desired resolution can be achieved in a given measurement setup.
References
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Andreas Kirsch,N I Grinberg +1 more
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Characterization of the shape of a scattering obstacle using the spectral data of the far field operator
TL;DR: In this article, the authors derived a factorization of the far field operator F in the form and proved that the ranges of and G coincide, and gave an explicit characterization of the scattering obstacle which uses only the spectral data of F. This result is used to prove a convergence result for a recent numerical method proposed by Colton, Kirsch, Monk, Piana and Potthast.
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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.