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Special Semester on Quantitative Biology analyzed by Mathematical Methods
Linz, October 1, 2007 - January 27, 2008
CONDUCTIVITY IMAGING USING ELECTRICAL IMPEDANCE TOMOGRAPHY AND ELASTIC DEFORMATION

Workshop on Bioimaging I, Mon, 12 Nov, 2007

Speaker: Jerome Fehrenbach

Abstract

Electrical impedance tomography (EIT) is an imaging technique that uses
Cauchy data to reconstruct the conductivity in a domain. On the practical point of view the task is difficult.

A new hybrid imaging technique that combines boundary electrical
measurements and elastic deformation inside the domain is under
investigation (Ammari et al., to appear). A small spherical deformation is induced by ultrasound around a point x in the domain. Using asymptotic estimates, the electrical power in a small domain around the point x is recovered from the variation of the boundary measures. More information is then available than in classical EIT, since measures are available inside the domain and not only on the boundary.

We present an algorithm to reconstruct the conductivity, assuming the
measured data is the energy density at each point of the domain. The
cost-function is the L2 distance between the measured and the predicted
energy density. The direct and adjoint derivatives of the energy density
with respect to the conductivity distribution are calculated. The
reconstruction algorithm uses a multigrid approach: at a coarse level the Jacobian of the cost function is assembled. At a fine level a Gauss-Newton optimization is implemented without computing the Jacobian matrix, using direct and adjoint differentiation. We also present numerical results on synthetical data.

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