EIT Reconstruction Algorithms: Pitfalls, Challenges and Recent Developments

We review developments, issues and challenges in Electrical Impedance Tomography (EIT), for the 4th Workshop on Biomedical Applications of EIT, Manchester 2003. We focus on the necessity for three dimensional data collection and reconstruction, efficient solution of the forward problem and present and future reconstruction algorithms. We also suggest common pitfalls or ``inverse crimes'' to avoid.Comment: A review paper for the 4th Workshop on Biomedical Applications of EIT, Manchester, UK, 200

Limited Angle Acousto-Electrical Tomography

This paper considers the reconstruction problem in Acousto-Electrical Tomography, i.e., the problem of estimating a spatially varying conductivity in a bounded domain from measurements of the internal power densities resulting from different prescribed boundary conditions. Particular emphasis is placed on the limited angle scenario, in which the boundary conditions are supported only on a part of the boundary. The reconstruction problem is formulated as an optimization problem in a Hilbert space setting and solved using Landweber iteration. The resulting algorithm is implemented numerically in two spatial dimensions and tested on simulated data. The results quantify the intuition that features close to the measurement boundary are stably reconstructed and features further away are less well reconstructed. Finally, the ill-posedness of the limited angle problem is quantified numerically using the singular value decomposition of the corresponding linearized problem.Comment: 23 page

Electrical Resistance Tomography of Conductive Thin Films

The Electrical Resistance Tomography (ERT) technique is applied to the measurement of sheet conductance maps of both uniform and patterned conductive thin films. Images of the sheet conductance spatial distribution, and local conductivity values are obtained. Test samples are tin oxide films on glass substrates, with electrical contacts on the sample boundary, some samples are deliberately patterned in order to induce null conductivity zones of known geometry while others contain higher conductivity inclusions. Four-terminal resistance measurements among the contacts are performed with a scanning setup. The ERT reconstruction is performed by a numerical algorithm based on the total variation regularization and the L-curve method. ERT correctly images the sheet conductance spatial distribution of the samples. The reconstructed conductance values are in good quantitative agreement with independent measurements performed with the van der Pauw and the four-point probe methods.Comment: IEEE Transactions on Instrumentation and Measuremen

Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography

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

Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT

In this paper, we develop a shape optimization-based algorithm for the electrical impedance tomography (EIT) problem of determining a piecewise constant conductivity on a polygonal partition from boundary measurements. The key tool is to use a distributed shape derivative of a suitable cost functional with respect to movements of the partition. Numerical simulations showing the robustness and accuracy of the method are presented for simulated test cases in two dimensions