Computational approaches in electrical impedance tomography with applications to head imaging

This thesis considers computational approaches to address the inverse problem arising from electrical impedance tomography (EIT), where the aim is to reconstruct (useful information about) the conductivity distribution inside a physical body from boundary measurements of current and voltages. The problem is nonlinear and highly ill-posed, and it generally presents several theoretical and numerical challenges. In fact, the search for a solution usually requires either carefully selected regularization techniques or simplifying assumptions on the measurement setting. A particular focus is on applying EIT to stroke detection in medical imaging, where measurement and modelling errors considerably deteriorate the available boundary data. To model these uncertainties, a novel computational three-dimensional head model is introduced and utilized to simulate realistic synthetic electrode measurements. According to the studied application, different models for the forward problem are considered, such as the continuum model, the complete electrode model and its smoothened version. The examined solution strategies correspond to different methodologies, ranging from regularized iterative reconstruction algorithms to machine learning techniques. The performance of these methods is assessed via three-dimensional simulated experiments performed in different settings.