INTERNATIONAL JOURNAL OF INFORMATION AND SYSTEMS SCIENCES Volume 2, Number 4, Pages 585-606 ©2006 Institute for Scientific Computing and Information MAGNETIC INDUCTION TOMOGRAPHY: SINGLE-STEP SOLUTION OF THE 3-D INVERSE PROBLEM FOR DIFFERENTIAL IMAGE RECONSTRUCTION HERMANN SCHARFETTER, PATRICIA BRUNNER AND ROBERT MERWA Abstract Magnetic induction tomography (MIT) is a low-resolution imaging modality used for reconstructing in 3-D the changes of the complex electrical conductivity in a target object. The measurement principle is based on determining the perturbation ∆B of a primary alternating magnetic field B0, which is coupled from an array of excitation coils to the object under investigation. The corresponding voltages ∆V and V0 induced in a receiver coil carry the information about the conductivity distribution. Potential medical applications comprise the continuous, non-invasive monitoring of tissue alterations which are reflected in the change of the conductivity, such as edema formation, ventilation disorders, wound healing and ischemic processes. MIT requires the solution of an inverse eddy current problem in three dimensions. which is underdetermined, ill-posed and non-linear in the parameters. Absolute imaging requires an iterative solution and suffers from heavy difficulties due to the comparatively low signal/noise ratio (SNR) of available MIT systems. Alternatively differential imaging is much easier and reconstruction can be done with single-step approaches. In this paper regularized single-step Gauss-Newton solutions are shown for state-differential and frequency differential protocols for both simulated and real data. Data were generated for 16 excitation coils and 32 receiver coils with a model of two spherical perturbations within a cylindrical saline tank. Simulated data were generated with a finite-element forward solver and random noise was added. The real data were obtained with an experimental MIT-system. Four different regularization matrices were compared: identity matrix (IM), neighbourhood matrix (NM), truncated singular value decomposition (TSVD) and variance uniformization (VU). A Monte-Carlo study was carried out in order to compare the statistical properties of the reconstruction results. Both simulated and real conductivity perturbations inside a homogeneous cylinder could be localized and resolved for an SNR between 44 and 64 dB. The VU method outperformed all other methods with respect to localization accuracy, resolution and edge sharpness, but, on the other hand, produced larger variance in the images. Frequency differential imaging allows the reconstruction of relative conductivity spectra which can be interpreted quantitatively. Key words: magnetic induction tomography, conductivity imaging, inverse problem, regularization, differential imaging 585