Fine-tuning electrode information in electrical impedance tomography

Dardé, Jérémi; Hakula, Harri; Hyvönen, Nuutti; Staboulis, Stratos

doi:10.3934/ipi.2012.6.399

Cited by 37 publications

(91 citation statements)

References 27 publications

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“…We perform the needed differentiations by resorting to the appropriate Fréchet derivatives of the (non-discretized) CEM (cf. [7,8]); in addition to reducing the computational load, this leads to higher stability compared to perturbation-based numerical differentiation schemes.…”

Section: Introduction Electrical Impedance Tomography (Eit)mentioning

confidence: 99%

“…which is linear with respect to the first and the third variable, can be sampled as indicated by the following proposition that is a slight generalization of [7,Corollary 4.2]. Proposition 2.3.…”

Section: Introduction Electrical Impedance Tomography (Eit)mentioning

confidence: 99%

“…Electrode shape derivatives. We start by recalling from [7] a general way of perturbing the electrodes {E m } M m=1 with the help of C 1 vector fields living on ∂E. We denote…”

Section: Introduction Electrical Impedance Tomography (Eit)mentioning

confidence: 99%

“…[7,Theorem 4.1]) that R is Fréchet differentiable with respect to the first variable at the origin. The corresponding derivative…”

Section: Introduction Electrical Impedance Tomography (Eit)mentioning

confidence: 99%

“…According to [7,Proposition 3.1], there exist d > 0 such that for any a ∈ B d , the formula (2.18) defines a set of well separated bounded and connected electrodes E a 1 , . .…”

Section: Introduction Electrical Impedance Tomography (Eit)mentioning

confidence: 99%

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Optimizing Electrode Positions in Electrical Impedance Tomography

Hyvönen¹,

Seppänen²,

Staboulis³

2014

SIAM J. Appl. Math.

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Abstract. Electrical impedance tomography is an imaging modality for recovering information about the conductivity inside a physical body from boundary measurements of current and voltage. In practice, such measurements are performed with a finite number of contact electrodes. This work considers finding optimal positions for the electrodes within the Bayesian paradigm based on available prior information on the conductivity; the aim is to place the electrodes so that the posterior density of the (discretized) conductivity, i.e., the conditional density of the conductivity given the measurements, is as localized as possible. To make such an approach computationally feasible, the complete electrode forward model of impedance tomography is linearized around the prior expectation of the conductivity, allowing explicit representation for the (approximate) posterior covariance matrix. Two approaches are considered: minimizing the trace or the determinant of the posterior covariance. The introduced optimization algorithm is of the steepest descent type, with the needed gradients computed based on appropriate Fréchet derivatives of the complete electrode model. The functionality of the methodology is demonstrated via two-dimensional numerical experiments.Key words. Electrical impedance tomography, optimal electrode locations, Bayesian inversion, complete electrode model, optimal experiment design AMS subject classifications. 65N21, 35Q60, 62F151. Introduction. Electrical impedance tomography (EIT) is an imaging modality for recovering information about the electrical conductivity inside a physical body from boundary measurements of current and potential. In practice, such measurements are performed with a finite number of contact electrodes. The reconstruction problem of EIT is a highly nonlinear and illposed inverse problem. For more information on the theory and practice of EIT, we refer to the review articles [3,5,36] and the references therein.The research on optimal experiment design in EIT has mostly focused on determining optimal current injection patterns. The most well-known approach to optimizing current injections is based on the distinguishability criterion [17], i.e., maximizing the norm of the difference between the electrode potentials corresponding to the unknown true conductivity and a known reference conductivity distribution. Several variants of the distinguishability approach have been proposed; see, e.g., [24,26] for versions with constraints on the injected currents. The application of the method to planar electrode arrays was considered in [22]. The distinguishability criterion leads to the use of current patterns generated by exciting several electrodes simultaneously. For other studies where the sensitivity of the EIT measurements is controlled by injecting currents through several electrodes at a time, see [32,39]. In geophysical applications of EIT, the data is often collected using four-point measurements; choosing the optimal ones for different electrode settings was studied in [1,10,34,38]...

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Section: Introduction Electrical Impedance Tomography (Eit)mentioning

confidence: 99%

Section: Introduction Electrical Impedance Tomography (Eit)mentioning

confidence: 99%

“…Electrode shape derivatives. We start by recalling from [7] a general way of perturbing the electrodes {E m } M m=1 with the help of C 1 vector fields living on ∂E. We denote…”

Section: Introduction Electrical Impedance Tomography (Eit)mentioning

confidence: 99%

“…[7,Theorem 4.1]) that R is Fréchet differentiable with respect to the first variable at the origin. The corresponding derivative…”

Section: Introduction Electrical Impedance Tomography (Eit)mentioning

confidence: 99%

“…According to [7,Proposition 3.1], there exist d > 0 such that for any a ∈ B d , the formula (2.18) defines a set of well separated bounded and connected electrodes E a 1 , . .…”

Section: Introduction Electrical Impedance Tomography (Eit)mentioning

confidence: 99%

See 3 more Smart Citations

Optimizing Electrode Positions in Electrical Impedance Tomography

Hyvönen¹,

Seppänen²,

Staboulis³

2014

SIAM J. Appl. Math.

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Linearly constrained minimum variance spatial filtering for localization of conductivity changes in electrical impedance tomography

Fernandez-Corazza

Ellenrieder

Muravchik

2015

Numer Methods Biomed Eng

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We localize dynamic electrical conductivity changes and reconstruct their time evolution introducing the spatial filtering technique to electrical impedance tomography (EIT). More precisely, we use the unit-noise-gain constrained variation of the distortionless-response linearly constrained minimum variance spatial filter. We address the effects of interference and the use of zero gain constraints. The approach is successfully tested in simulated and real tank phantoms. We compute the position error and resolution to compare the localization performance of the proposed method with the one-step Gauss-Newton reconstruction with Laplacian prior. We also study the effects of sensor position errors. Our results show that EIT spatial filtering is useful for localizing conductivity changes of relatively small size and for estimating their time-courses. Some potential dynamic EIT applications such as acute ischemic stroke detection and neuronal activity localization may benefit from the higher resolution of spatial filters as compared to conventional tomographic reconstruction algorithms.

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Spectral shape optimization for the Neumann traces of the Dirichlet-Laplacian eigenfunctions

2019

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We consider a spectral optimal design problem involving the Neumann traces of the Dirichlet-Laplacian eigenfunctions on a smooth bounded open subset Ω of IR n . The cost functional measures the amount of energy that Dirichlet eigenfunctions concentrate on the boundary and that can be recovered with a bounded density function.We first prove that, assuming a L 1 constraint on densities, the so-called Rellich functions maximize this functional.Motivated by several issues in shape optimization or observation theory where it is relevant to deal with bounded densities, and noticing that the L ∞ -norm of Rellich functions may be large, depending on the shape of Ω, we analyze the effect of adding pointwise constraints when maximizing the same functional. We investigate the optimality of bang-bang functions and Rellich densities for this problem. We also deal with similar issues for a close problem, where the cost functional is replaced by a spectral approximations. Finally, this study is completed by the investigation of particular geometries and is illustrated by several numerical simulations.Keywords: wave equation, boundary observability, shape optimization, calculus of variations, spectrum of the laplacian, quantum ergodicity at the boundary.

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Fine-tuning electrode information in electrical impedance tomography

Cited by 37 publications

References 27 publications

Optimizing Electrode Positions in Electrical Impedance Tomography

Optimizing Electrode Positions in Electrical Impedance Tomography

Linearly constrained minimum variance spatial filtering for localization of conductivity changes in electrical impedance tomography

Spectral shape optimization for the Neumann traces of the Dirichlet-Laplacian eigenfunctions

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