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 ...

In optical tomography a physical body is illuminated with near-infrared light and the resulting outward photon flux is measured at the object boundary. The goal is to reconstruct internal optical properties of the body, such as absorption and diffusivity. In this work, it is assumed that the imaged object is composed of an approximately homogeneous background with clearly distinguishable embedded inhomogeneities. An algorithm for finding the maximum a posteriori estimate for the absorption and diffusion coefficients is introduced assuming an edge-preferring prior and an additive Gaussian measurement noise model. The method is based on iteratively combining a lagged diffusivity step and a linearization of the measurement model of diffuse optical tomography with priorconditioned LSQR. The performance of the reconstruction technique is tested via threedimensional numerical experiments with simulated measurement data.

Electrical impedance tomography aims at reconstructing the conductivity inside a physical body from boundary measurements of current and voltage at a finite number of contact electrodes. In many practical applications, the shape of the imaged object is subject to considerable uncertainties that render reconstructing the internal conductivity impossible if they are not taken into account. This work numerically demonstrates that one can compensate for inaccurate modeling of the object boundary in two spatial dimensions by estimating the locations and sizes of the electrodes as a part of a reconstruction algorithm. The numerical studies, which are based on both simulated and experimental data, are complemented by proving that the employed complete electrode model is approximately conformally invariant, which suggests that the obtained reconstructions in mismodeled domains reflect conformal images of the true targets. The numerical experiments also confirm that a similar approach does not, in general, lead to a functional algorithm in three dimensions.