Simultaneous recovery of admittivity and body shape in electrical impedance tomography: an experimental evaluation

Dardé, Jérémi; Hyvönen, Nuutti; Seppänen, Aku; Staboulis, Stratos

doi:10.1088/0266-5611/29/8/085004

Cited by 41 publications

(84 citation statements)

References 36 publications

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“…In addition to the piecewise linear FEM basis functions, the quadratic Lagrange elements are used for comparison; for general information on properties and advantages of FEMs of different types and order, we refer to the textbook [20] and the references therein. Two pairs of conductivities and contact conductances are considered: the first one corresponds to σ/ζ el ≈ 50 · 10 −3 m, i.e., the peak in the top right plot in Figure 2, whereas the second pair results in σ/ζ el ≈ 4·10 −3 m, which roughly corresponds to the values mentioned in [7]. The conductance half-heights ζ el for the smoothened model are computed as in the bottom plot of Figure 2 and they are σ/ζ el ≈ 30·10 −3 m and σ/ζ el ≈ 0.5·10 −3 m, respectively.…”

Section: 2mentioning

confidence: 82%

“…When the CEM is employed, the contact conductances (or admittances, resistances, or impedances) are usually not known, but they are estimated along with the interior conductivity [11]. One may also simultaneously reconstruct the electrode locations and the shape of the imaged object [6,7,24]. However, even if all these parameters were known, an inherent property of the traditional CEM is that the employed "discontinuous" Robin-type boundary condition causes the regularity of the electromagnetic potential to be limited, namely, it is of the Sobolev class H 2− , > 0.…”

Section: Introductionmentioning

confidence: 99%

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Smoothened Complete Electrode Model

Hyvönen¹,

Mustonen²

2017

SIAM J. Appl. Math.

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Abstract. This work reformulates the complete electrode model of electrical impedance tomography in order to enable more efficient numerical solution. The model traditionally assumes constant contact conductances on all electrodes, which leads to a discontinuous Robin boundary condition since the gaps between the electrodes can be described by vanishing conductance. As a consequence, the regularity of the electromagnetic potential is limited to less than two square-integrable weak derivatives, which negatively affects the convergence of, e.g., the finite element method. In this paper, a smoothened model for the boundary conductance is proposed, and the unique solvability and improved regularity of the ensuing boundary value problem are proven. Numerical experiments demonstrate that the proposed model is both computationally feasible and also compatible with real-world measurements. In particular, the new model allows faster convergence of the finite element method.

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Section: 2mentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Smoothened Complete Electrode Model

Hyvönen¹,

Mustonen²

2017

SIAM J. Appl. Math.

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“…However, the analysis in [9,16] is based on the assumption that the electrodes stretch accordingly when the shape of Ω changes. For cylindrical domains, as are the ones considered in [9,10], compensating for such stretching is straightforward because an electrode is essentially determined by its two end points; see [9]. However, in our inherently three-dimensional setting, analyzing how the changes in the sizes and shapes of the electrodes affect the shape derivatives becomes more complicated, and we choose to leave such consideration for future studies.…”

Section: 4mentioning

confidence: 99%

“…We start by briefly reviewing the reconstruction algorithm that is based on a simple Gauss-Newton iteration; for more information consult, e.g., [10,15]. Next, we explain how realistic measurement data are simulated.…”

Section: Numerical Experiments This Section Presents Our Numerical Ementioning

confidence: 99%

“…In this work we extend the conceptually straightforward way of handling imprecisely known body shape and electrode positions introduced in [8,9,10]. The basic idea is to utilize the derivatives of the electrode potentials with respect to the exterior boundary shape and the electrode locations in a regularized Newton-type output least squares algorithm that simultaneously reconstructs all unknowns in the measurement setup.…”

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confidence: 99%

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Computational Framework for Applying Electrical Impedance Tomography to Head Imaging

Candiani¹,

Hannukainen²,

Hyvönen³

2019

SIAM J. Sci. Comput.

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This work introduces a computational framework for applying absolute electrical impedance tomography to head imaging without accurate information on the head shape or the electrode positions. A library of fifty heads is employed to build a principal component model for the typical variations in the shape of the human head, which leads to a relatively accurate parametrization for head shapes with only a few free parameters. The estimation of these shape parameters and the electrode positions is incorporated in a regularized Newton-type output least squares reconstruction algorithm. The presented numerical experiments demonstrate that strong enough variations in the internal conductivity of a human head can be detected by absolute electrical impedance tomography even if the geometric information on the measurement configuration is incomplete to an extent that is to be expected in practice.

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Generalized linearization techniques in electrical impedance tomography

Hyvönen

Mustonen

2018

Numer. Math.

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Electrical impedance tomography aims at reconstructing the interior electrical conductivity from surface measurements of currents and voltages. As the current-voltage pairs depend nonlinearly on the conductivity, impedance tomography leads to a nonlinear inverse problem. Often, the forward problem is linearized with respect to the conductivity and the resulting linear inverse problem is regarded as a subproblem in an iterative algorithm or as a simple reconstruction method as such. In this paper, we compare this basic linearization approach to linearizations with respect to the resistivity or the logarithm of the conductivity. It is numerically demonstrated that the conductivity linearization often results in compromised accuracy in both forward and inverse computations. Inspired by these observations, we present and analyze a new linearization technique which is based on the logarithm of the Neumannto-Dirichlet operator. The method is directly applicable to discrete settings, including the complete electrode model. We also consider Fréchet derivatives of the logarithmic operators. Numerical examples indicate that the proposed method is an accurate way of linearizing the problem of electrical impedance tomography.n. hyvönen and l. mustonen 2 respect to the conductivity can be computed explicitly [4,14,18]. By applying the chain rule of Banach spaces, or via direct computation, it is possible to consider derivatives with respect to the resistivity or the logarithm of the conductivity as well. In this paper, we compare the linearization errors resulting from these different input parametrizations of the electrical properties. We also discuss the corresponding methods for the complete electrode model (CEM), which is an accurate model for practical EIT measurements [5,21].As the main novelty, we introduce the logarithm of the Neumann-to-Dirichlet operator and use its differentiability properties to construct a new linearization method for EIT. Loosely speaking, the traditional forward operator is replaced by an operator that maps the logarithm of the conductivity to the logarithm of the boundary potentials, the latter being understood in a sense of linear operators. The corresponding least squares inversion algorithm then fits the computed logarithmic potentials to the logarithm of the measurement matrix. Although this logarithmic forward operator is still nonlinear, numerical experiments show that the resulting linearization errors are in most cases smaller than with any other considered linearization method.This paper is organized as follows. In Section 2, the continuum forward model of EIT and the related Neumann-to-Dirichlet operator are reviewed. We write the dependence of the Neumannto-Dirichlet operator on the electrical properties in three different ways and recall also the corresponding Fréchet derivatives. Section 3 presents the formal definition for the logarithm of the Neumann-to-Dirichlet operator and studies its differentiability and other properties as an unbounded operator on the space of square-integ...

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Simultaneous recovery of admittivity and body shape in electrical impedance tomography: an experimental evaluation

Cited by 41 publications

References 36 publications

Smoothened Complete Electrode Model

Smoothened Complete Electrode Model

Computational Framework for Applying Electrical Impedance Tomography to Head Imaging

Generalized linearization techniques in electrical impedance tomography

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