The Linearized Inverse Problem in Multifrequency Electrical Impedance Tomography

Alberti, Giovanni S.; Ammari, Habib; Jin, Bangti; Seo, Jiyeon; Zhang, Wenlong

doi:10.1137/16m1061564

Cited by 39 publications

(44 citation statements)

References 59 publications

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“…In the reconstruction procedure of [28], a certain infinite matrix is truncated, which is philosophically close to our truncation of that Fourier-like series. We refer to [1,9,11] for numerical studies of DN. In [5] and [12] reconstruction procedures for DN for hyperbolic PDEs were developed, and they were computationally tested in [6] and [12,13] respectively.…”

Section: Introductionmentioning

confidence: 99%

Convexification of restricted Dirichlet-to-Neumann map

Klibanov

2017

Journal of Inverse and Ill-Posed Problems

118

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By our definition, "restricted Dirichlet-to-Neumann map" (DN) means that the Dirichlet and Neumann boundary data for a Coefficient Inverse Problem (CIP) are generated by a point source running along an interval of a straight line. On the other hand, the conventional DN data can be generated, at least sometimes, by a point source running along a hypersurface. CIPs with the restricted DN data are nonoverdetermined in the n−D case with n ≥ 2. We develop, in a unified way, a general and a radically new numerical concept for CIPs with restricted DN data for a broad class of PDEs of the second order, such as, e.g. elliptic, parabolic and hyperbolic ones. Namely, using Carleman Weight Functions, we construct globally convergent numerical methods. Hölder stability and uniqueness are also proved. The price we pay for these features is a well acceptable one in the Numerical Analysis: we truncate a certain Fourier-like series with respect to some functions depending only on the position of that point source. At least three applications are: imaging of land mines, crosswell imaging and electrical impedance tomography.

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Section: Introductionmentioning

confidence: 99%

Convexification of restricted Dirichlet-to-Neumann map

Klibanov

2017

Journal of Inverse and Ill-Posed Problems

118

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“…Below, we describe a group sparse reconstruction method developed in [2] to solve the ill-conditioned linear systems (2.11) and (2.12).…”

Section: )mentioning

confidence: 99%

“…These linear systems are often under-determined, and severely ill-conditioned, due to the inherent ill-posed nature of the DOT inverse problem. We adapt a numerical sparse method developed in [2] to solve (2.15). The algorithm takes the following two aspects into consideration:…”

Section: Group Sparse Reconstruction Algorithmmentioning

confidence: 99%

Linearized reconstruction for diffuse optical spectroscopic imaging

2019

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In this paper, we present a novel reconstruction method for diffuse optical spectroscopic imaging with a commonly used tissue model of optical absorption and scattering. It is based on linearization and group sparsity, which allows recovering the diffusion coefficient and absorption coefficient simultaneously, provided that their spectral profiles are incoherent and a sufficient number of wavelengths are judiciously taken for the measurements. We also discuss the reconstruction for imperfectly known boundary and show that with the multi-wavelength data, the method can reduce the influence of modelling errors and still recover the absorption coefficient. Extensive numerical experiments are presented to support our analysis.Mathematics Subject Classification (MSC2000). 94A08, 35R30, 92C55.

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“…Introduction. Multifrequency electrical impedance tomography (mfEIT) [2,6,19,22] can be applied to the noninvasive assessment of abdominal obesity, which is a predictor of health risk. mfEIT data of the boundary current-voltage relationship at various frequencies of < 1 MHz reflect the regional distribution of body fat, which is less conductive than water and tissues such as muscle, and can therefore be used to estimate the thicknesses of visceral and subcutaneous adipose tissue [13].…”

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confidence: 99%

“…, N E [25] as shown in Figure 2.2. It is worth emphasizing that the solution u h k depends on the electrode radius h. Let P denote a set of indexes (k + , k − , l + , l − ) indicating inject-measure electrodes; e.g., (1,2,3,4) means that the electrodes E 1 , E 2 are used for current injection and the electrodes E 3 , E 4 are used for voltage measurements. In the static EIT, the measured data U h k,l is used as a voltage difference:…”

mentioning

confidence: 99%

Mathematical Framework for Abdominal Electrical Impedance Tomography to Assess Fatness

Ammari¹,

Kwon²,

Lee³

et al. 2017

SIAM J. Imaging Sci.

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Abstract. This paper presents a static electrical impedance tomography (EIT) technique that evaluates abdominal obesity by estimating the thickness of subcutaneous fat. EIT has a fundamental drawback for absolute admittivity imaging because of its lack of reference data for handling the forward modeling errors. To reduce the effect of boundary geometry errors in imaging abdominal fat, we develop a depth-based reconstruction method that uses a specially chosen current pattern to construct reference-like data, which are then used to identify the border between subcutaneous fat and muscle. The performance of the proposed method is demonstrated by numerical simulations using 32-channel EIT system and a humanlike domain.

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The Linearized Inverse Problem in Multifrequency Electrical Impedance Tomography

Cited by 39 publications

References 59 publications

Convexification of restricted Dirichlet-to-Neumann map

Convexification of restricted Dirichlet-to-Neumann map

Linearized reconstruction for diffuse optical spectroscopic imaging

Mathematical Framework for Abdominal Electrical Impedance Tomography to Assess Fatness

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