## The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc. | |

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission
of the Department of Engineering Physics and Mathematics for public examination and debate in
Auditorium K at Helsinki University of Technology (Espoo, Finland)
on the 14^{th} of May, 2004, at 12 o'clock noon.

Overview in PDF format (ISBN 951-22-7086-2) [283 KB]

Dissertation is also available in print (ISBN 951-22-7068-4)

This thesis presents mathematical analysis of optical and electrical impedance tomography. We introduce papers [I-III], which study these diffusive tomography methods in the situation where the examined object is contaminated with inclusions that have physical properties differing from the background.

This thesis consists of an overview and of the following 3 publications:

- Hyvönen N., 2002. Analysis of optical tomography with non-scattering regions. Proceedings of the Edinburgh Mathematical Society 45, number 2, pages 257-276.
- Hyvönen N., 2004. Complete electrode model of electrical impedance tomography: approximation properties and characterization of inclusions. SIAM Journal on Applied Mathematics 64, number 3, pages 902-931. © 2004 Society for Industrial and Applied Mathematics (SIAM). By permission.
- Hyvönen N., 2004. Characterizing inclusions in optical tomography. Inverse Problems 20, number 3, pages 737-751. © 2004 Institute of Physics Publishing Ltd. By permission.

**Keywords:**
inverse boundary value problems, variational principles, optical tomography,
non-scattering regions, radiative transfer equation, diffusion approximation,
electrical impedance tomography, inverse conductivity problem, electrode
models, inclusions, factorization method

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© 2004 Helsinki University of Technology

Last update 2011-05-26