Email: kaipio@venda.uku.fi

CompanyName: University of Kuopio

Country: FINLAND

Abstract: Optimality of current patterns
with

respect to posterior covariance measures

The theory of optimal current patterns
that

is based on Isaacson's distinguishability

criterion has been proved to be very

successful. In the framework of statistical

interpretation of inverse problems this

criterion is related to maximizing the

difference between the associated likelihood

densities. Although regularization is usually

employed and we strictly speaking can not

refer to the likelihood, this approach works

very well in most such situations that are

usually considered. However, with respect to

the theory of statistical inverse problems,

criteria that focus on likelihood densities

are not relevant. Rather, the final aim is

to consider posterior densities and measures.

In this paper we formulate the optimal current

pattern problem in the statistical inverse

problems setting by considering optimality

with respect to measures on posterior

covariance. These measures are directly

related to estimation error, that is, the

accuracy of the actual conductivity estimates.

The determination of the optimal current

patterns is not based on the actual (or

guessed) conductivity distribution of the

target but rather on the prior density of the

target. We discuss several examples and show

that the optimal current patterns that

correspond to the distinguishability criterion

are usually good also with respect to the

posterior criteria especially when the prior

covariances are diagonal and the reference

conductivity distribution is known. However,

with more complex prior densities it can be

difficult or impossible to construct the two

densities that the distinguishability criterion

is based on. However, for theses densities

of classes the determination of the optimal

current patterns with respect to the posterior

measures is straightforward.