Single-step 3-D image reconstruction in magnetic induction tomography: Theoretical limits of spatial resolution and contrast to noise ratio

Magnetic induction tomography (MIT) is a low-resolution imaging modality for reconstructing the changes of the complex conductivity in an object. MIT is based on determining the perturbation of an alternating magnetic field, which is coupled from several excitation coils to the object. The conductivity distribution is reconstructed from the corresponding voltage changes induced in several receiver coils. Potential medical applications comprise the continuous, non-invasive monitoring of tissue alterations which are reflected in the change of the conductivity, e.g. edema, ventilation disorders, wound healing and ischemic processes. MIT requires the solution of an ill-posed inverse eddy current problem. A linearized version of this problem was solved for 16 excitation coils and 32 receiver coils with a model of two spherical perturbations within a cylindrical phantom. The method was tested with simulated measurement data. Images were reconstructed with a regularized single-step Gauss-Newton approach. Theoretical limits for spatial resolution and contrast/noise ratio were calculated and compared with the empirical results from a Monte-Carlo study. The conductivity perturbations inside a homogeneous cylinder were localized for a SNR between 44 and 64dB. The results prove the feasibility of difference imaging with MIT and give some quantitative data on the limitations of the method.