Direct inversion from partial-boundary data in electrical impedance tomography

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http://hdl.handle.net/10138/307552

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Hauptmann , A , Santacesaria , M & Siltanen , S 2017 , ' Direct inversion from partial-boundary data in electrical impedance tomography ' , Inverse Problems , vol. 33 , no. 2 , 025009 . https://doi.org/10.1088/1361-6420/33/2/025009

Title: Direct inversion from partial-boundary data in electrical impedance tomography
Author: Hauptmann, Andreas; Santacesaria, Matteo; Siltanen, Samuli
Other contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics

Date: 2017-02
Language: eng
Number of pages: 26
Belongs to series: Inverse Problems
ISSN: 0266-5611
DOI: https://doi.org/10.1088/1361-6420/33/2/025009
URI: http://hdl.handle.net/10138/307552
Abstract: In electrical impedance tomography (EIT) one wants to image the conductivity distribution of a body from current and voltage measurements carried out on its boundary. In this paper we consider the underlying mathematical model, the inverse conductivity problem, in two dimensions and under the realistic assumption that only a part of the boundary is accessible to measurements. In this framework our data are modeled as a partial Neumann-to-Dirichlet map (ND map). We compare this data to the full-boundary ND map and prove that the error depends linearly on the size of the missing part of the boundary. The same linear dependence is further proved for the difference of the reconstructed conductivities-from partial and full boundary data. The reconstruction is based on a truncated and linearized D-bar method. Auxiliary results include an extrapolation method to estimate the full-boundary data from the measured one, an approximation of the complex geometrical optics solutions computed directly from the ND map as well as an approximate scattering transform for reconstructing the conductivity. Numerical verification of the convergence results and reconstructions are presented for simulated test cases.
Subject: inverse conductivity problem
electrical impedance tomography
Neumann-to-Dirichlet map
partial-boundary data
D-bar method
D-BAR METHOD
LESS REGULAR CONDUCTIVITIES
PARTIAL CAUCHY DATA
CALDERON PROBLEM
GLOBAL UNIQUENESS
DOMAIN TRUNCATION
ELECTRODE MODEL
PLANE
RECONSTRUCTION
STABILITY
111 Mathematics
114 Physical sciences
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