2017
DOI: 10.1137/16m1068888
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Polynomial Collocation for Handling an Inaccurately Known Measurement Configuration in Electrical Impedance Tomography

Abstract: Abstract. The objective of electrical impedance tomography is to reconstruct the internal conductivity of a physical body based on measurements of current and potential at a finite number of electrodes attached to its boundary. Although the conductivity is the quantity of main interest in impedance tomography, a real-world measurement configuration includes other unknown parameters as well: the information on the contact resistances, electrode positions and body shape is almost always incomplete. In this work,… Show more

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Cited by 15 publications
(22 citation statements)
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“…Derivative with respect to β. To begin with, let us consider a general way of perturbing the shapes and sizes of the electrodes; see [8,14] for more information. Assume the portion of ∂Ω to which the electrodes are attached is of class C 2 .…”
Section: 3mentioning
confidence: 99%
See 1 more Smart Citation
“…Derivative with respect to β. To begin with, let us consider a general way of perturbing the shapes and sizes of the electrodes; see [8,14] for more information. Assume the portion of ∂Ω to which the electrodes are attached is of class C 2 .…”
Section: 3mentioning
confidence: 99%
“…To put it short, the error caused by the mismodeling was included as an extra additive noise process in the measurement model, its statistics were estimated in advance based on heavy simulations and prior knowledge on all unknown parameters, and finally the actual inversion was performed within the Bayesian paradigm. Recently, [14] built a polynomial surrogate for the dependence of the boundary measurements of EIT on all unknowns, including the parametrized measurement geometry, and employed this surrogate in straightforward Tikhonov regularization in two spatial dimensions. Of the aforementioned methods, the ones introduced in [21,22] and [14] have only been implemented in two spatial dimensions, and the approximation error approach employed in [27,28] requires a vast and expressive teaching sample describing the possible types of geometric mismodeling.…”
mentioning
confidence: 99%
“…Moreover, the employment of a parametric model simplifies the handling of the unknown boundary shape (cf. [5,6,11]).…”
Section: Pseudospectral Approximationmentioning
confidence: 99%
“…for some coefficients β (k) m,i ∈ R that can be obtained by expanding the expression in (11). Among the not-yet-selected multi-indices, the one corresponding to the largest -norm has (loosely speaking) affected the approximation most and thus can be considered the critical index, whose admissible forward neighbors are added to the index set.…”
Section: Adaptive Spammentioning
confidence: 99%
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