Regularized Reconstruction in Electrical

This article describes a new approach to reconstruction of the conductivity eld in electrical impedance tomography. Our goal is to improve the trade-oo between the quality of the images and the numerical complexity of the reconstruction method. In order to reduce the computational load, we adopt a linearized approximation to the forward problem that describes the relationship between the unknown conductivity and the measurements. In this framework, we focus on nding a proper way to cope with the ill-posed nature of the problem mainly caused by strong attenuation phenomena; this is done by devising regulariza-tion techniques well suited to this particular problem. First, we propose a solution which is based on Tikhonov regularization of the problem. Second, we introduce an original regularized reconstruction method in which the regular-ization matrix is determined by space-uniformization of the variance of the reconstructed condictivities. Both methods are non-supervised, i.e., all tuning parameters are automatically determined from the measured data. Tests performed on simulated and real data indicate that Tikhonov regularization provides results similar to those obtained with iterative methods, but with a much smaller amount of computations. Regularization using a variance uniformization constraint yields further improvements, particularly in the central region of the unknown object where attenuation is most severe. We anticipate that the variance uniformization approach could be adapted to iterative methods that preserve the nonlinearity of the forward problem. More generally, it appears as a useful tool for solving other severely ill-posed reconstruction problems such as eddy current tomography.