Electrical property tomography (EPT) reconstructs the human body’s conductivity and relative permittivity using the radio frequency field from a magnetic resonance machine. Since conductivity and relative permittivity can be biomarkers for many illnesses, it is necessary to reconstruct them accurately. To this end, this thesis focuses on the two-dimensional tranceive phase corrected contrast source inversion algorithm (2D-CSI).

This 2D-CSI algorithm is significantly faster than its three-dimensional (3D) counterpart. However, reconstruction artefacts may appear since the 2D field description is not always applicable. In this thesis, these artefacts are identified and it is investigated if the 2D-CSI algorithm can be improved to handle them. In particular, the proposed updates are, first, implementing the early stopping principle, then adding a positivity constraint to the conductivity and relative permittivity, and lastly, initialising with Helmholtz electrical property tomography (HEPT). The first two enhancements create a more robust algorithm, while the third update could be useful only in specific cases (with no fine structures and low noise levels).

After achieving a more robust algorithm, the 2D-CSI algorithm is applied to the realistic 3D dataset ”A Database for MR-based Electrical Properties Tomography” (ADEPT). The first and foremost challenge is accurately simulating the incident field, as the reconstructions depend a lot on the incident fields. If the incident fields do not match perfectly, the algorithm can only produce satisfactory reconstruction results in a part of the reconstruction domain. The reconstructions are only partly accurate because the reconstructed electric fields converge to a line creating line artefacts. It is shown that small changes in the incident fields produce small changes in the position of the artefacts. Based on this observation, a reconstruction strategy has been developed in which a reconstruction without artefacts is produced by combining reconstruction results of multiple incident fields. Integrating all modifications of the 2D-CSI
algorithm in one single framework shows that the conductivity and relative permittivity of the brain in the middle of the birdcage coil can be reconstructed accurately

The tissue electrical properties of conductivity and permittivity affect the interactions of electromagnetic fields in the body. These properties vary throughout the different tissues as the tissue structure and composition varies. In this thesis, medical imaging and diagnosis is used as primary example to motivate exploration of a novel regularization approach to an MRI-based electrical properties tomography (EPT) method.

Total variation (TV) regularization has been shown to perform noise reduction in the iterative Contrast Source Inversion EPT (CSI-EPT) method. The Jacobi matrix inversion regularization, an alternative to the known conjugate gradient formulation, is elaborated and applied to an E-polarized MRI fields scenario such that this thesis presents the Jacobi step regularized CSI-EPT.

The alternative regularization method outperforms the known regularization method in the reconstruction qualities of noise-suppression and edge-preservation in the simulated MRI experiments using a virtual body model. Further advancements are also described, such as multiple inner-iterations Jacobi regularization and an anatomical prior initialization of the contrast function. Important future research topics are the incorporation and evaluation of the Jacobi step regularization into more advanced CSI-EPT versions, which are the three-dimensional and transceive phase based algorithms to correct realistic MRI data.

A system has been developed that utilises the techniques of Ultra Wideband and Synthetic Aperture Radar to produce top view images of a scene using measurements from the side. The system consists of the PulsON P410 radar module, a set of antennas, a moving platform and an imaging algorithm. This thesis will cover all the aspects of the data acquisition part of the system with additionally an analysis on antennas.