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.

Atrial fibrillation (AF) is the most common type of cardiac arrhythmia occurring in around 0.5% of the world population. AF is characterized by the rapid and irregular beating of the atrial chambers of the heart, which can cause lead to strokes and other heart-failures. To prevent these consequences the early detection of AF is paramount. Using photoplethysmography (PPG) heart activity can be measured from which the inter-beat-interval (IBI), the time between heart beats, can be estimated. Using data collected by a PPG sensor the aim is to classify the heart activity as either AF or Normal Sinus Rhythm in real time using machine learning and collect the outcomes for further analysis by medical professionals. For this a classification method is suggested which is able to be implemented on an ARM based processor. Using a Support Vector Machine and 10 features derived from the IBI's and the PPG signal this algorithm achieves the following accuracy metrics: balanced accuracy = 0.853, sensitivity = 0.850, specificity = 0.856 and Matthews Correlation Coefficient (MCC) = 0.643. Compared to similar studies these results are substandard and should be improved.