Inverse Problems for Magnetic Induction Tomography

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Magnetic Induction Tomography (MIT) is a relatively new, non-invasive imaging technique which has applications in both industrial and clinical settings. In essence, it is capable of reconstructing the electromagnetic parameters (permittivity, permeability and conductivity) of an object from measurements made on its surface. An MIT device consists of two sets of coils placed around the boundary of the object to be imaged. The first set of coils is used for the purpose of excitation, and by passing a current through each coil in turn, a primary magnetic field is created. The second set of coils is then used for measurement. This procedure causes an eddy current when each of the primary magnetic fields interacts with a conducting body inducing secondary magnetic fields, and hence voltages, that are measured in the second set of coils.Enabling MIT to take the step from being an experimental technique, which has already received some clinical interest, to become a viable imaging technique for the detection and monitoring of conditions, such as cerebral stroke, requires a step change in the quality of the reconstruction of the electromagnetic parameters and, therefore, an improvement of the computational approach used for the solution of the inverse problem. To achieve this we propose to solve the inverse Maxwell problem with a variational algorithm. Although a proof of concept of this work exists, in order to make this algorithm effective in a clinical environment, and hence applicable to the MIT problem, an implementation using high performance computing is needed, this research proposal aims to address this issue.