Public defence in Mathematics, M.Sc. (Tech) Topi Kuutela

Title of the doctoral thesis: Computational and theoretical models in diffuse imaging

Opponent: Professor Bastian von Harrach, Goethe-University Frankfurt, Germany
Custos: Professor Nuutti Hyvönen, Aalto University School of Science, Department of Mathematics and Systems Analysis

The doctoral thesis is publicly displayed 10 days before the defence in the publication archive Aaltodoc of Aalto University.

Electronic thesis

Public defence announcement:

In many sub fields of sciences and engineering, computational models are used to describe the behavior of, and to produce predictions on the considered system. Typically the models are constructed directly from the fundamental physics of the system, or out of well-justified simplifications of these natural laws. However, this often forces the scientist to make choices between mathematically equivalent options, and that cannot be easily justified.

In this doctoral thesis the effects of some modeling choices are studied in the context of mathematical models for two imaging modalities. The studied modalities are modeled as mathematical inverse problems. More precisely, they are modeled as parameter estimation problems in which the internal material distribution is estimated based on measurements made on the surface of the object. The unit of considered material parameter represents one such hard-to-justify choice. For example, in impedance tomography the primary parameter of interest is the internal electrical conductivity, which can be parametrized as either resistivity or as conductivity, i.e. the reciprocal value of resistivity. Although both options lead to mathematically similar problems, the choice has a significant impact on the final material distribution estimate.

This work introduces new modeling approaches and considers the error sensitivity in the mathematical modeling of impedance tomography and diffuse optical tomography. The new approaches may help with mitigating some of the most important error sources in the estimation of the material field. The error sensitivity analysis considers the opposite side of the coin, considering how much do certain error sources affect the material distribution estimate. The introduced methods may help in development of more accurate or robust computational methods for the considered imaging modalities.

Contact details of the doctoral student: [email protected]