Fourier analysis in Magnetic Induction Tomography: Mapping of anisotropic, inhomogeneous resistivity

Magnetic Induction Tomography is an electromagnetic-based technique for mapping the passive electromagnetic properties of conductors and has the potential for applications in biomedical imaging. In a previous analysis we approached the inverse problem of determining isotropic resistivity with a Fourier-based analysis. Here, we extend that analysis to anisotropic media. The proposed Fourier-based solution method, when properly filtered, robustly handles noise to accurately map the inhomogeneous terms of the resistivity tensor. We observe a random variation in the measure of accuracy (mean deviation) that is resolved with independent spatial frequencies in the x- and y-directions in the applied field. Further, the formation of improper images we noted in our previous analysis is addressed through this use of independent spatial frequencies and through the use of additional applied fields. We conclude with a discussion of computation time for the large system of linear equations this method requires and propose methods for limiting memory usage.