Minisymposia Abstracts

Speaker: Nuutti Hyvönen
Aalto University, Helsinki, Finland
Title: Justification of a point electrode model in electrical impedance tomography
Abstract: The most accurate model for real-life electrical impedance tomography is the complete electrode model, which takes into account electrode shapes and (usually unknown) contact impedances at electrode-object interfaces. When the electrodes are small, however, it is tempting to formally replace them by point sources. In this work we rigorously justify such a point electrode model for the important case of having difference measurements ("relative data") as data for the reconstruction problem. We do this by deriving the asymptotic limit of the complete model for vanishing electrode size. The feasibility of our approach is also demonstrated by numerical examples.

Speaker: Tanja Tarvainen
University of Eastern Finland, Kuopio, Finland
Title: Corrections to linear methods in diffuse optical tomography using approximation error modelling
Abstract: In diffuse optical tomography (DOT), linearization is typically built from analytic Green's functions which solve the diffusion approximation in predetermined domain such as an infinite space. These linear methods are limited by the fact that they cannot predict large changes in the optical parameters and that they assume the background optical properties to be known. However, such methods have been found to produce good quality images in situations in which these limitations are fulfilled and a reference measurement from known background medium is available.

In this work we examine the correction of errors when using a first order Born approximation with an infinite space Green's function model as the basis for linear reconstruction in DOT, when real data is generated on a finite domain with possibly unknown background optical properties. We consider the relationship between conventional reference measurement correction and Bayesian approximation error modelling in reconstruction. We develop an approach in which the approximation error approach is used to correct the linear reconstruction method in DOT. It is shown that, using the approximation error modelling, linear reconstruction method can be used to produce good quality images also in situations in which the background optical properties are not known and a reference is not available.

This is joint work with V. Kolehmainen, J.P. Kaipio and S.R. Arridge.

Speaker: Ville Kolehmainen
University of Eastern Finland
Title: Marginalization of uninteresting distributed parameters in inverse problems – Application to diffuse optical tomography
Abstract: With inverse problems there are often several unknown distributed parameters of which only one may be of interest. Since assigning incorrect fixed values to the uninteresting parameters usually leads to a severely erroneous model, one is forced to estimate all distributed parameters simultaneously. This may increase the computational complexity of the problem significantly. In the Bayesian framework, all unknowns are generally treated as random variables and estimated simultaneously and all uncertainties can be modelled systematically. Recently, the approximation error approach has been proposed for handling uncertainty and model reduction related errors in the models. In this approach, approximate marginalization of these errors is carried out before the estimation of the interesting variables. In this paper, we discuss the adaptation of the approximation error approach to the marginalization of uninteresting distributed parameters. As an example, we consider the marginalization of scattering coefficient in diffuse optical tomography.

Speaker: Ting Wei
Lanzhou University, China
Title: Numerical studies for the moving boundary identification in the inverse heat conduction problem
Abstract: In this talk, we present some numerical methods for recovering a moving boundary from Cauchy data in a one or two dimensional heat problem.

The numerical methods include a method of fundamental solutions and a method of lines. To obtain a stable approximate moving boundary, various regularization techniques and choice rules on regularization parameters are used. The uniqueness of moving boundary is also given under some assumptions.

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