Public examination of a doctoral dissertation in the field of physics

Doctoral candidate: M.Sc. Antti Nissinen

Date and venue: 3.6.2011 at 12 noon, L22, Snellmania, Kuopio campus

**ABSTRACT**

In electrical impedance tomography (EIT), electrodes are attached on the boundary of the object and currents are injected into the object. The voltages are measured using the same electrodes and the conductivity of the object is reconstructed based on the measured voltages. The reconstruction problem is a non-linear ill-posed inverse problem, i.e. the problem is highly sensitive to measurement and approximation errors. The effect of the measurement errors can be reduced by using an accurate measurement system and by accurate modeling of the statistics of the error.

Approximation errors are due to an approximative computational model used in the inverse computations. In practical applications, an adequately accurate mathematical model cannot often be used due to limited computational resources, and therefore a reduced model has to be used. Furthermore, in some cases the accurate model is not available due to unknown shape of the body or unknown nuisance parameters in the computation model, for example. These approximation errors can cause severe reconstruction errors with conventional measurement error models.

Recently, the approximation error approach was proposed for the treatment of the approximation errors. The key idea in the approximation error approach is to represent the approximation errors as a noise process in the measurement model. The statistical model of the approximation error is constructed and then this model is used in the inverse problem to compensate for the approximation errors.

In this thesis, the approximation error approach is applied for several approximation errors in EIT. The approximation errors that are considered are due to reduced discretization, unknown contact impedances, domain truncation and unknown shape of the body. Furthermore, the approximation error approach is employed in a novel way enabling estimation of the conductivity and the shape of the body. All test cases are evaluated by using simulated and real data. The results indicate that the effect of these errors can be efficiently compensated for by the approximation error approach.

The doctoral dissertation of Antti Nissinen entitled “*Modelling Errors in Electrical Impedance Tomography” *will be examined at the Faculty of Science and Forestry. The opponent in the public examination is **Samuli Siltanen** from the University of Helsinki and the custos is Professor **Marko Vauhkonen** of the University of Eastern Finland.

Photo available for download at http://www.uef.fi/vaitoskuvat

**Contact:** Antti Nissinen, tel. +358 40 741 9102, antti.nissinen@uef.fi

Publishing year: 2011

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