Explicit Characterization of Inclusions in Electrical Impedance Tomography

Brühl, Martin

doi:10.1137/s003614100036656x

Cited by 124 publications

(209 citation statements)

References 15 publications

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“…Remark 2 shows how this criterion becomes operative. This theorem can be proved following the lines of the proof of [10, Theorem 6.8] that treats the case of constant σ B (see also [19]). The only point that requires attention is the use of unique continuation arguments for equations of type (2), and this is why a regularity assumption on σ B is required.…”

Section: The Factorization Methods With Deterministic Inhomogeneous Bamentioning

confidence: 99%

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Numerical analysis of the factorization method for EIT with a piecewise constant uncertain background

Haddar¹,

Migliorati²

2013

Inverse Problems

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Abstract. We extend the Factorization Method for Electrical Impedance Tomography to the case of background featuring uncertainty. We first describe the algorithm for known but inhomogeneous backgrounds and indicate expected accuracy from the inversion method through some numerical tests. Then we develop three methodologies to apply the Factorization Method to the more difficult case of piece-wise constant but uncertain background. The first one is based on a recovery of the background through an optimization scheme and is well adapted to relatively low dimensional random variables describing the background. The second one is based on a weighted combination of the indicator functions provided by the Factorization Method for different realizations of the random variables describing the uncertain background. We show through numerical experiments that this procedure is well suited to the case where many realizations of the measurement operators are available. The third strategy is a variant of the previous one when measurements for the inclusion-free background are available. In that case, a single pair of measurements is sufficient to achieve comparable accuracy to the deterministic case.

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Section: The Factorization Methods With Deterministic Inhomogeneous Bamentioning

confidence: 99%

“…The optimal value of α is computed plugging (19) into the nonlinear equation (20), and solving with respect to α. To show the inversion results, we display the isolines of the indicator function…”

Section: Description Of the Algorithm For The Deterministic Settingmentioning

confidence: 99%

Numerical analysis of the factorization method for EIT with a piecewise constant uncertain background

Haddar¹,

Migliorati²

2013

Inverse Problems

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“…Linear sampling methods [24,131,71] have a similar time complexity and advantages as the monotonicity method. While still applied to piecewise constant conductivities, linear sampling methods can handle any number of discrete conductivity values provided the anomalies separated from each other by the background.…”

Section: Direct Non-linear Methodsmentioning

confidence: 99%

The reconstruction problem

Lionheart¹,

Polydorides²,

Borsic³

2004

Series in Medical Physics and Biomedical Engineering

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“…Moreover, the convergence cannot be guaranteed [24]. An alternative method to form EIT images is by using direct reconstruction methods, such as the D-bar, linear modeling, and strip line just to mention a few [24,[33][34][35]. These approaches form a distribution map of the conducting domain without iteratively solving a series of forward problems.…”

Section: The Monotonicity Principlementioning

confidence: 99%

A Bimodal Reconstruction Method for Breast Cancer Imaging

Flores-Tapia¹,

O’Halloran²,

Pistorius³

2011

PIER

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Abstract-Breast Microwave Radar (BMR) has been proposed as an alternative modality for breast imaging. This technology forms a reflectivity map of the breast region by illuminating the scan area using ultra wide band microwave waveforms and recording the reflections from the breast structures. Nevertheless, BMR images require to be interpreted by an experienced practitioner since the location and density of the breast region can make the detection of malignant lesions a difficult task. In this paper, a novel bimodal breast imaging reconstruction method based on the use of BMR and Electrical Impedance Tomography (EIT) is proposed. This technique forms an estimate of the breast region impedance map using its corresponding BMR image. This estimate is used to initialize an EIT reconstruction method based on the monotonicity principle. The proposed method yielded promising results when applied to MRI-derived numeric breast phantoms.

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Explicit Characterization of Inclusions in Electrical Impedance Tomography

Cited by 124 publications

References 15 publications

Numerical analysis of the factorization method for EIT with a piecewise constant uncertain background

Numerical analysis of the factorization method for EIT with a piecewise constant uncertain background

The reconstruction problem

A Bimodal Reconstruction Method for Breast Cancer Imaging

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