Numerical implementation of two noniterative methods for locating inclusions by impedance tomography

By Martin Brühl, Martin Hanke. 2000

225 citations recorded by the source corpus.

Subfields: Electrical and Electronic Engineering, Geophysics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9bfd669b424fd520d9c01e93279c9e0473d96ac0

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Citations in the corpus

The Factorization Method for Real Elliptic Problems (2006, methodology): “Such an identity was originally developed by Kirsch for Inverse Scattering is known for this diffusion example (Kirsch), also with Robin B.C. (Hyvönen), Electrostatics (Hähner), EIT (Brühl, Hanke), also with different electrode models (Brühl, Hanke, Hyvönen) and in the half space (Schappel).”
Electrical impedance tomography using level set representation and total variational regularization (2005, methodology): “Brühl and Hanke [4] proposed a method based on an explicit criterion of whether a point is lying inside or outside of a certain set to solve the impedance tomography.”
The linear sampling method in inverse electromagnetic scattering theory (2003, methodology): “Applications of the linear sampling method to practical problems have been considered in microwave tomography, in the case of the detection of leukaemia in human bone marrow [19], in impedance tomography [ 3 ], in elasticity [1, 12, 23, 47] and for the detection of buried objects [14].”
Multiple level set methods with applications for identifying piecewise constant functions (2004, background): “There are a variety of medical problems for which it would be useful to know the time-varying distribution of electrical properties inside a human body [ 2 , 16, 19, 41].”
REGULARIZED D-BAR METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM (2009, unknown): “Other cgo-based algorithms have been developed for detection of inclusions, for example see [15, 37, 38, 88].”
Monotonicity and local uniqueness for the Helmholtz equation (2017, background): “…originally developed for scattering problems involving far-field measurements of the Helmholtz equation by Kirsch [1998], see also [Kirsch and Grinberg 2008], and then extended to the inverse conductivity problem in [Brühl and Hanke 2000; Brühl 2001]; see also the overview article [Harrach 2013].”
Electrical impedance tomography (2002, background): “For example, in [31, 85], Brühl and Hanke image the inclusions B j inside as follows: let Gx0,z solve (in the sense of distributions) the differential equation”