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Title of the thesis: Polynomial techniques in electrical impedance tomography

Thesis defender: Markus Hirvensalo
Opponent: Accosiate Professor Luca Rondi, Università degli Studi di Pavia, Italy
Custos: Professor Nuutti Hyvönen, Aalto University School of Science

The dissertation examines electrical impedance tomography (EIT), which is an imaging method and, in its theoretical formulation, an inverse problem. The problem is approached from the perspective of how the idealized theory of EIT corresponds to the numerical approximations used in practice, where measurement data, resolution, and computational resources are unavoidably limited.

The aim of the research is to determine which theoretical properties of EIT remain meaningful in discretized models and which, in turn, require reinterpretation. At the same time, the goal is to understand how practical constraints influence the formulation and analysis of theoretical models.

The topic lies within the field of inverse problems, which combines functional analysis, partial differential equations, and numerical computation. Although EIT is a widely studied method, the relationship between its idealized theory and practical computational models is still only partially understood.

The main results are related to the compactness of linearized operators arising in EIT, constructing their extensions to suitable Hilbert spaces, and developing recursive methods that reflect practical reconstruction algorithms. The research provides new insights into how the mathematical theory of EIT and its numerical implementation can be aligned. The results help to identify which theoretical assumptions are justified in practice and how computational limitations should be taken into account in modeling.

Keywords: Electrical impedance tomography, Inverse problems, Polynomial techniques

Thesis available for public display 7 days prior to the defence at .