Name: Elena Cherkaev

Email: elena@math.utah.edu

CompanyName: University of Utah

Country: U.S.A.

Abstract: Multiscale EIT for imaging of a random medium

by Elena Cherkaev
University of Utah

In many heterogeneous materials such as porous media, biological
materials, and artificial composites, the fine scale of the
microstructure cannot be resolved by applied electric field,
and the response of the medium is homogenized. The talk
discusses an approach to EIT imaging which ties
together properties of the medium on two different scales:
Complex permittivity found on the coarse scale imaging
step provide data for microscale inversion which recovers
information about the fine structure of the random medium.
Information about the microgeometry is contained in the spectral
measure in the Stieltjes integral representation of the
effective complex permittivity of the medium. The problem
of reconstruction of the spectral measure has unique solution,
however it is extremely ill-posed. Several stabilization
techniques are discussed such as quadratically constrained
minimization, regularization using nonnegativity constraint,
and reconstruction in the class of functions of bounded variation.
The reconstructed spectral function can be used to estimate
geometric parameters of the structure as well as to evaluate
other effective properties of the same medium, such as thermal
or hydraulic conductivity.

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