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 currentto-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.
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 Fréchet 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.
The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it was shown that a simple monotonicity property of the related Neumann-to-Dirichlet map can be used to characterize shapes of inhomogeneities in a known background conductivity. In this paper we formulate a monotonicity-based shape reconstruction scheme that applies to approximative measurement models, and regularizes against noise and modelling error. We demonstrate that for admissible choices of regularization parameters the inhomogeneities are detected, and under reasonable assumptions, asymptotically exactly characterized. Moreover, we rigorously associate this result with the complete electrode model, and describe how a computationally cheap monotonicity-based reconstruction algorithm can be implemented. Numerical reconstructions from both simulated and real-life measurement data are presented.
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.Key words. Electrical impedance tomography, priorconditioning, edge-preferring regularization, LSQR, complete electrode model AMS subject classifications. 65N21, 35R301. Introduction. The aim of electrical impedance tomography is to reconstruct the internal conductivity distribution of a physical body based on boundary measurements of current and voltage. This constitutes a nonlinear and severely illposed inverse problem. EIT can be used in medical imaging, process tomography and nondestructive testing of materials. Consult the review articles [2, 10, 33] for more information on EIT, the associated mathematical theory and the related reconstruction algorithms. In this work, we consider EIT under the prior assumption that the tobe-reconstructed conductivity consists of well defined inclusions in an approximately homogeneous background, which is a setting encountered in many practical applications: Consider, e.g., the localization of air bubbles or manufacturing defects in a piece of building material. We work exclusively with the complete electrode model (CEM), which is the most accurate model for real-world EIT [11,32]; in particular, the introduced algorithm also estimates the contact resistances that are an unavoidable nuisance of practical EIT.We tackle the reconstruction problem of EIT within the Bayesian paradigm and incorporate the prior information on the structure of the imaged object by introducing an edge-preferring prior density for the (discretized) conductivity. The prior for the contact resistances is chosen to be uninformative since their estimation from EIT measurements is not an illposed problem. Assuming an additive Gaussian measurement noise model, the computation of the maximum a posteriori (MAP) estimate, i.e., the maximizer of the posterior density, corresponds to finding a minimizer for a Tikhonovtype functional that exhibits nonquadratic behavior in both the discrepancy and the penalty term. In the terminology of regularization theory, this corresponds ...
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