Edge-Enhancing Reconstruction Algorithm for Three-Dimensional Electrical Impedance Tomography

Abstract

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 ...

Electrode modelling: The effect of contact impedance

“…The problem can be tackled e.g. by applying CEM-based iterative (Newton-type) methods which allow estimating both the conductivity distribution and the contact impedances [15,26,27]. In this technique, a subtlety arises if a physical contact impedance is very close to zero, as numerical approximation of the CEM is known to turn unstable in the limit [24].…”

Stochastic Galerkin Finite Element Method with Local Conductivity Basis for Electrical Impedance Tomography

“…As the examples consider inclusions that are either insulating (plastic) or highly conducting (steel), the interval [0.2, 2.0] mS for the conductivity values may seem a bit restrictive. However, according to our experience (cf., e.g., [8,14]), 0.2 mS is a sufficiently low value for modeling an insulating object accurately enough and, on the other hand, highly conducting objects exhibit some resistivity in EIT, probably due to the contact resistance at their boundaries (cf. [15]).…”

Image Reconstruction in Electrical Impedance Tomography Based on Structure-Aware Sparse Bayesian Learning

“…A finitedimensional approximation of the Whittle-Matérn priors is derived from sparse inverse covariance matrices by using a stochastic partial differential equation. The problem considered in [37] is to reconstruct the conductivity consisting of well-defined inclusion-type targets in an approximately homogeneous background. The proposed iterative algorithm is based on the use of a nonlinear edge-preferring prior density and the minimization of the corresponding Tikhonov functional by efficiently solving an approximate sequence of linearized problems with the help of prior-conditioning and least squares with QR factorization (LSQR).…”