Simultaneous Reconstruction of Outer Boundary Shape and Admittivity Distribution in Electrical Impedance Tomography

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

doi:10.1137/120877301

Cited by 40 publications

(84 citation statements)

References 31 publications

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“…Recently, new computational methods for recovering from the uncertainty of the boundary shape have been developed. 24,25 These methods allow for quantitative imaging and do not require reference data. A drawback, of course, is the computational burden associated with the iterative solution of the nonlinear inverse problem, and again, decreasing the computation time by model reduction would be very beneficial.…”

Section: Introductionmentioning

confidence: 99%

Electrical impedance tomography imaging with reduced-order model based on proper orthogonal decomposition

Lipponen

Seppänen

Kaipio

2013

J. Electron. Imaging

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Electrical impedance tomography (EIT) is an imaging modality in which the conductivity distribution inside a target is reconstructed based on voltage measurements from the target's surface. Reconstructing the conductivity distribution is known to be an illposed inverse problem whose solutions are highly intolerant to modeling errors. To achieve sufficient accuracy, very dense meshes are usually needed in a finite element approximation of the EIT forward model. This leads to very high-dimensional problems and often unacceptably tedious computations for real-time applications. We consider the model reduction in EIT within the Bayesian inversion framework. We construct the reduced-order model by proper orthogonal decompositions (POD) of the electrical conductivity and the potential distributions. The associated POD modes are computed based on a priori information on the conductivity. The feasibility of the reduced-order model is tested both numerically and with experimental data. The proposed approach is shown to speed up EIT reconstruction considerably without significantly decreasing image quality. In the selected test cases, high-quality reconstructions are obtained with the reduced-order model in 3.5% to 5% of the time required for conventional reconstructions.

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Section: Introductionmentioning

confidence: 99%

Electrical impedance tomography imaging with reduced-order model based on proper orthogonal decomposition

Lipponen

Seppänen

Kaipio

2013

J. Electron. Imaging

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“…Take note that the chosen noise covariance is such that the expected |V sim − R(σ draw )I| 2 is about 0.005 2 |R(σ * )I| 2 , i.e., it roughly corresponds to 0.5% of relative error. Subsequently, for each V sim , an (approximate) MAP estimate, determined by (3.2) where the posterior density is the unlinearized one from (3.7), is computed by a variant of the Gauss-Newton algorithm (see, e.g., [8]). …”

Section: Numerical Examplesmentioning

confidence: 99%

“…The extent of this latter effect depends heavily on the complexity of the object shape. (iii) Choosing optimal electrode locations results in improved solutions to the (nonlinear) inverse problem of EIT -at least, for our Bayesian reconstruction algorithm (see, e.g., [8]) and if the target conductivity is drawn from the assumed prior density.…”

Section: Introduction Electrical Impedance Tomography (Eit)mentioning

confidence: 99%

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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“…the cross-section of a human torso is close to an ellipse, using a circular geometry for inversion introduces heavy artifacts which make it impossible to reconstruct anything meaningful if the geometry is not adjusted properly (cf. [DHSS13]). Unfortunately, analytic expressions of conformal maps and their normal derivatives from arbitrary simply connected domains to the unit disk are usually not available.…”

Section: 4mentioning

confidence: 99%

Resolution-Controlled Conductivity Discretization in Electrical Impedance Tomography

Winkler¹,

Rieder²

2014

SIAM J. Imaging Sci.

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Simultaneous Reconstruction of Outer Boundary Shape and Admittivity Distribution in Electrical Impedance Tomography

Cited by 40 publications

References 31 publications

Electrical impedance tomography imaging with reduced-order model based on proper orthogonal decomposition

Electrical impedance tomography imaging with reduced-order model based on proper orthogonal decomposition

Optimizing Electrode Positions in Electrical Impedance Tomography

Resolution-Controlled Conductivity Discretization in Electrical Impedance Tomography

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