Recent Progress on the Factorization Method for Electrical Impedance Tomography

Harrach, Bastian

doi:10.1155/2013/425184

Cited by 52 publications

(47 citation statements)

References 31 publications

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“…Several reconstruction methods have been proposed for anomaly or inclusion detection problems, cf., e.g., Potthast [34] for an overview. Arguably, the most prominent inclusion detection method is the Factorization Method (FM) of Kirsch, Brühl and Hanke [35]- [37], see [14], [38]- [53] for the devolopment of the FM in the field of EIT and [54] for a recent overview. Notably, in the overview [54] , the FM is formulated on the basis of monotonicity-based arguments, and the recent result [55] indicates that, for EIT, the FM can be outperformed by monotonicity-based methods first formulated by Tamburrino and Rubinacci in [56], [57].…”

Section: Introductionmentioning

confidence: 99%

Resolution Guarantees in Electrical Impedance Tomography

Harrach

Ullrich

2015

IEEE Trans. Med. Imaging

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Electrical impedance tomography (EIT) uses current-voltage measurements on the surface of an imaging subject to detect conductivity changes or anomalies. EIT is a promising new technique with great potential in medical imaging and non-destructive testing. However, in many applications, EIT suffers from inconsistent reliability due to its enormous sensitivity to modeling and measurement errors. In this work, we show that it is principally possible to give rigorous resolution guarantees in EIT even in the presence of systematic and random measurement errors. We derive a constructive criterion to decide whether a desired resolution can be achieved in a given measurement setup. Our results cover the case where anomalies of a known minimal contrast in a subject with imprecisely known background conductivity are to be detected from noisy measurements on a number of electrodes with imprecisely known contact impedances. The considered settings are still idealized in the sense that the shape of the imaging subject has to be known and the allowable amount of uncertainty is rather low. Nevertheless, we believe that this may be a starting point to identify new applications and to design and optimize measurement setups in EIT.

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Section: Introductionmentioning

confidence: 99%

Resolution Guarantees in Electrical Impedance Tomography

Harrach

Ullrich

2015

IEEE Trans. Med. Imaging

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“…Second, the method has only been justified for the definite case (or that the domain can be split into two a-priori known regions with the definiteness property, cf. Schmitt [44] and the review [14]).…”

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Monotonicity-Based Shape Reconstruction in Electrical Impedance Tomography

Harrach¹,

Ullrich²

2013

SIAM J. Math. Anal.

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Current-voltage measurements in electrical impedance tomography can be partially ordered with respect to definiteness of the associated self-adjoint Neumann-to-Dirichlet operators (NtD). With this ordering, a point-wise 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 (aka 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. † Birth name: Bastian Gebauer,

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“…An explicit reconstruction formula that is based on the global uniqueness proof of Nachman [62] is known as the d-bar method, cf., e.g., [70,51,52,55,46,56,47,53,54]. Rigorously justified inclusion detection methods for EIT include the enclosure method (see [41,10,42,44,43,45,39,74,38]), the Factorization Method (see [21,14,49,4,24,37,57,63,16,15,18,29,66,31,67,17,11,13,6] and the recent overviews [50,23,27]), and the recently emerging Monotonicity Method [72,71,32,76].…”

Section: Introductionmentioning

confidence: 99%

Interpolation of missing electrode data in electrical impedance tomography

Harrach

2015

Inverse Problems

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Novel reconstruction methods for electrical impedance tomography (EIT) often require voltage measurements on current-driven electrodes. Such measurements are notoriously difficult to obtain in practice as they tend to be affected by unknown contact impedances and require problematic simultaneous measurements of voltage and current.In this work, we develop an interpolation method that predicts the voltages on current-driven electrodes from the more reliable measurements on current-free electrodes for difference EIT settings, where a conductivity change is to be recovered from difference measurements. Our new method requires the a-priori knowledge of an upper bound of the conductivity change, and utilizes this bound to interpolate in a way that is consistent with the special geometry-specific smoothness of difference EIT data.Our new interpolation method is computationally cheap enough to allow for realtime applications, and simple to implement as it can be formulated with the standard sensitivity matrix. We numerically evaluate the accuracy of the interpolated data and demonstrate the feasibility of using interpolated measurements for a monotonicitybased reconstruction method.

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Recent Progress on the Factorization Method for Electrical Impedance Tomography

Cited by 52 publications

References 31 publications

Resolution Guarantees in Electrical Impedance Tomography

Resolution Guarantees in Electrical Impedance Tomography

Monotonicity-Based Shape Reconstruction in Electrical Impedance Tomography

Interpolation of missing electrode data in electrical impedance tomography

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