The EIDORS (electrical impedance and diffuse optical reconstruction software) project aims to produce a software system for reconstructing images from electrical or diffuse optical data. MATLAB is a software that is used in the EIDORS project for rapid prototyping, graphical user interface construction and image display. We have written a MATLAB package (http://venda.uku.fi/ vauhkon/) which can be used for two-dimensional mesh generation, solving the forward problem and reconstructing and displaying the reconstructed images (resistivity or admittivity). In this paper we briefly describe the mathematical theory on which the codes are based on and also give some examples of the capabilities of the package.

Inverse problems can be characterized as problems that tolerate measurement and modelling errors poorly. While the measurement error issue has been widely considered as a solved problem, the modelling errors have remained largely untreated. The approximation and modelling errors can, however, be argued to dominate the measurement errors in most applications. There are several applications in which the temporal and memory requirements dictate that the computational complexity of the forward solver be radically reduced. For example, in process tomography the reconstructions have to be carried out typically in a few tens of milliseconds. Recently, a Bayesian approach for the treatment of approximation and modelling errors for inverse problems has been proposed. This approach has proven to work well in several classes of problems, but the approach has not been verified in any problem with real data. In this paper, we study two different types of modelling errors in the case of electrical impedance tomography: one related to model reduction and one concerning partially unknown geometry. We show that the approach is also feasible in practice and may facilitate the reduction of the computational complexity of the nonlinear EIT problem at least by an order of magnitude.

In this paper, we examine how the estimation method of the electrode contact impedances proposed earlier works in two different laboratory experiments. In the first experiment, the performance of the method was studied for a tank filled with a homogeneous liquid. In this case a single parameter for the contact impedances was used. In the second experiment the method was tested with a single target within a tank. In this case the contact impedances on all the electrodes were estimated. It was found that in the two-electrode measurement protocol the estimation of the electrode contact impedances improves reconstructions substantially. If only a single electrode contact impedance value for all the electrodes was estimated it was found that in certain cases it was not adequate.

Inverse problems can be characterized as problems that tolerate measurement and modelling errors poorly. Typical sources of modelling errors include (pure) approximation errors related to numerical discretization, unknown geometry and boundary data, and possibly sensor locations. With electrical impedance tomography (EIT), the unknown contact impedances are an additional error source. Recently, a Bayesian approach to the treatment of approximation and modelling errors for inverse problems has been proposed. This approach has been shown to be applicable to a variety of modelling and approximation errors, at least with simulations. Recently, it was shown that recovery from significant model reduction and moderate mismodelling of geometry in EIT was also possible with laboratory EIT data. In this paper, we show that the errors due to the unknown contact impedances can also be compensated for by employing the approximation error approach. Furthermore, the recovery from simultaneous contact impedance, domain truncation and discretization-related errors is also feasible.

There are many different electrical impedance tomography (EIT) systems which are either non-commercial (in-house products) or commercial products. However, these systems are usually designed for specific applications and therefore the functionality of the systems might be limited. Nowadays there are commercially available many low-cost, efficient and accurate multifunctional components for data acquisition and signal processing. Therefore, it should be possible to construct an EIT system which is mainly built from commercially available components. The main goal of this work was to study the performance of a PXI-based EIT systemPCI eXtension for Instrumentation.. In this work, a PXI-based EIT system with 16 independent current injection channels and 80 independent measurement channels was constructed and tested. The results indicate that an EIT system can be constructed using a PXI platform which decreases the construction time of the system. Moreover, the system is efficient, accurate, modular, and it is not limited to any predetermined measurement protocols.