Inverse Problems for Magnetic Induction Tomography

磁感应断层成像(MIT)是一种相对较新的非侵入性成像技术，在工业和临床环境中都有应用。本质上，它能够根据物体表面的测量重建物体的电磁参数(介电常数、磁导率和电导率)。MIT设备由围绕待成像对象边界放置的两组线圈组成。第一组线圈用于励磁，通过依次通过每个线圈传递电流，产生初级磁场。然后使用第二组线圈进行测量。当每个初级磁场与导电体相互作用时产生涡流，从而产生在第二组线圈中测量的次级磁场和电压。使麻省理工学院能够从已经获得一些临床兴趣的实验技术迈出一步，成为用于检测和监测诸如中风等情况的可行成像技术，需要在电磁参数重建的质量上逐步改变，因此，改进用于解决逆问题的计算方法。为此，我们提出用变分算法求解麦克斯韦逆问题。虽然这项工作的概念存在证明，为了使该算法在临床环境中有效，从而适用于MIT问题，需要使用高性能计算的实现，本研究提案旨在解决这个问题。

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.