The D-bar method for electrical impedance tomography-demystified

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http://hdl.handle.net/10138/324385

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Mueller , J L & Siltanen , S 2020 , ' The D-bar method for electrical impedance tomography-demystified ' , Inverse Problems , vol. 36 , no. 9 , 093001 . https://doi.org/10.1088/1361-6420/aba2f5

Title: The D-bar method for electrical impedance tomography-demystified
Author: Mueller, J. L.; Siltanen, S.
Contributor: University of Helsinki, Inverse Problems
Date: 2020-09
Language: eng
Number of pages: 28
Belongs to series: Inverse Problems
ISSN: 0266-5611
URI: http://hdl.handle.net/10138/324385
Abstract: Electrical impedance tomography (EIT) is an imaging modality where a patient or object is probed using harmless electric currents. The currents are fed through electrodes placed on the surface of the target, and the data consists of voltages measured at the electrodes resulting from a linearly independent set of current injection patterns. EIT aims to recover the internal distribution of electrical conductivity inside the target. The inverse problem underlying the EIT image formation task is nonlinear and severely ill-posed, and hence sensitive to modeling errors and measurement noise. Therefore, the inversion process needs to be regularized. However, traditional variational regularization methods, based on optimization, often suffer from local minima because of nonlinearity. This is what makes regularized direct (non-iterative) methods attractive for EIT. The most developed direct EIT algorithm is the D-bar method, based on complex geometric optics solutions and a nonlinear Fourier transform. Variants and recent developments of D-bar methods are reviewed, and their practical numerical implementation is explained.
Subject: D-bar method
electrical impedance tomography
complex geometrical optics
direct reconstruction algorithm
NOVIKOV-VESELOV EQUATION
INVERSE CONDUCTIVITY PROBLEM
GLOBAL UNIQUENESS
SPATIAL PRIOR
INTEGRAL-EQUATION
SCATTERING METHOD
RECONSTRUCTIONS
ALGORITHM
TRANSFORM
ADMITTIVITIES
111 Mathematics
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