Electromagnetic tomography: Real-time imaging using linear approaches

The main objective of the present work consists in the development of linear image reconstruction algorithms for two tomographic technologies aimed for biomedical applications, the Magnetic Induction Tomography (MIT) and the Electrical Impedance Tomography (EIT). This required the implementation of numerical forward problem solvers, which simulate the interaction between a given electromagnetic field and a body with a specific conductivity distribution. A new subgridding scheme was developed for the MIT forward problem. Both solvers are fully automatic, requiring only the specification of the problem data and allow the obtainment of virtual measurements that can be used in the image reconstruction process. Regarding the inverse problems, different reconstruction algorithms were studied in order to get images in real-time. The Back-Projection and the Filtered Back-Projection methods were implemented, either along straight lines, or along magnetic flux lines (specifically for the MIT) or equipotential lines (specifically for EIT). The state of the art image reconstruction algorithm GREIT was also implemented and applied for the first time to the resolution of the 2D EIT and 3D MIT inverse problems. The results obtained were satisfying since they demonstrate the applicability of these technologies to the clinical environment.