Stratos Staboulis

Aalto University, Helsinki, Southern Finland Province, Finland

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Publications (6)1.9 Total impact

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    ABSTRACT: Electrical impedance tomography is an imaging modality for extracting information on the conductivity distribution inside a physical body from boundary measurements of current and voltage. In many practical applications, it is a priori known that the conductivity consists of embedded inhomogeneities in an approximately constant background. This work introduces an iterative reconstruction algorithm that aims at finding the maximum a posteriori estimate for the conductivity assuming an edge-preferring prior. The method is based on applying (a single step of) priorconditioned lagged diffusivity iteration to sequential linearizations of the forward model. The algorithm is capable of producing reconstructions on dense unstructured three-dimensional finite element meshes and with a high number of measurement electrodes. The functionality of the proposed technique is demonstrated with both simulated and experimental data in the framework of the complete electrode model, which is the most accurate model for practical impedance tomography.
    06/2014;
  • Nuutti Hyvönen, Aku Seppänen, Stratos Staboulis
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    ABSTRACT: 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 Fr\'echet derivatives of the complete electrode model. The functionality of the methodology is demonstrated via two-dimensional numerical experiments.
    04/2014;
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    Stratos Staboulis, Jérémi Dardé
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    ABSTRACT: Current-to-voltage measurements of electrical impedance tomography are accurately modelled by the {\em complete electrode model} which takes into account the contact impedance at the electrode/object interface. The formal limiting case is the {\em shunt model}, in which perfect contacts, that is, vanishing contact impedance is assumed. The main objective of this work is to study the relationship between these two models. In smooth geometry, we show that the energy norm discrepancy is almost of order square root of the contact impedance. In addition to this, we consider the discrepancy between the finite dimensional electrode potentials which are used as forward models in many practical applications: interpreting the shunt model as an orthogonal projection of the complete electrode model and applying a duality argument implies that this discrepancy decays twice as fast. We also demonstrate that in the limit, part of the Sobolev regularity of the spatial potential is lost; this possibly has the undesirable effect of slowing down the convergence of its numerical approximation. The theoretical results are backed up by two dimensional numerical experiments: one probing the asymptotic relationship between the models and another one testing the effect of the contact impedance on the finite element approximation of the complete electrode model.
    12/2013;
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    ABSTRACT: In this paper, the simultaneous retrieval of the exterior boundary shape and the interior admittivity distribution of an examined body in electrical impedance tomography is considered. The reconstruction method is built for the complete electrode model and it is based on the Fréchet derivative of the corresponding current-to-voltage map with respect to the body shape. The reconstruction problem is cast into the Bayesian framework, and maximum a posteriori estimates for the admittivity and the boundary geometry are computed. The feasibility of the approach is evaluated by experimental data from water tank measurements. The results demonstrate that the proposed method has potential for handling an unknown body shape in a practical setting.
    Inverse Problems 07/2013; 29(8):085004. · 1.90 Impact Factor
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    ABSTRACT: The aim of electrical impedance tomography is to reconstruct the admittivity distribution inside a physical body from boundary measurements of current and voltage. Due to the severe ill-posedness of the underlying inverse problem, the functionality of impedance tomography relies heavily on accurate modelling of the measurement geometry. In particular, almost all reconstruction algorithms require the precise shape of the imaged body as an input. In this work, the need for prior geometric information is relaxed by introducing a Newton-type output least squares algorithm that reconstructs the admittivity distribution and the object shape simultaneously. The method is built in the framework of the complete electrode model and it is based on the Fr\'echet derivative of the corresponding current-to-voltage map with respect to the object boundary shape. The functionality of the technique is demonstrated via numerical experiments with simulated measurement data.
    05/2012;
  • E Emi, Harri Hakula, Nuutti Hy Onen, Stratos Staboulis
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    ABSTRACT: Electrical impedance tomography is a noninvasive imaging technique for recovering the admittance distribution inside a body from boundary measurements of current and voltage. In practice, impedance tomography suffers from inaccurate modelling of the measurement setting: The exact electrode locations and the shape of the imaged object are not necessarily known precisely. In this work, we tackle the problem with imperfect electrode information by introducing the Fréchet derivative of the boundary measurement map of impedance tomography with respect to the electrode shapes and locations. This enables us to include the fine-tuning of the information on the electrode positions as a part of a Newton-type output least squares reconstruction algorithm; we demonstrate that this approach is feasible via a two-dimensional numerical example based on simulated data. The impedance tomography measurements are modelled by the complete electrode model, which is in good agreement with real-life electrode measurements.

Publication Stats

3 Citations
1.90 Total Impact Points

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Institutions

  • 2013
    • Aalto University
      • Department of Mathematics and Systems Analysis
      Helsinki, Southern Finland Province, Finland