zastosowania elektromagnetyzmu w nowoczesnych ... - PTZE

XVIII Sympozjum PTZE, Zamość 2008
LEVEL SET METHOD APPLIED
TO SHAPE MODELLING IN EIT
Przemysław Berowski 1 , Magdalena Stasiak 2
1 Electrotechnical Institute,
Pożaryskiego 28, 04-703 Warsaw, e-mail: p.berowski@iel.waw.pl
2 Department of Electrical Apparatus, Technical University of Lodz,
Stefanowskiego 18/22, 90-924 Lodz, e-mail: stasiak@p.lodz.pl
In our case the level set method approach in the inverse problem solution is used. The
model of the forward problem is consisted of two spatially homogenous areas with different
conductivity. The inverse problem solution provides the identification the position and the
shape of the inside object.
The inverse problem in Electrical Impedance Tomography (EIT) is highly nonlinear,
because the current flow strongly depends on the unknown conductivity within the object.
The solution of the inverse problem in EIT is significantly more difficult than e.g. X-ray
computed tomography, where the photon paths are essentially straight lines. Furthermore, the
problem is ill-posed due to its instability – small errors in the measurements can produce large
errors in reconstruction of conductivity. There are many different algorithms for inverse
problem solution: deterministic methods (e.g. back-projection, perturbation, and Newton-
Raphson, Conjugate Gradient method), stochastic methods (e.g. Genetic Algorithms, Monte-
Carlo method, Simulated Annealing, and also Artificial Neural Network (ANN).
Level set methods are proposed as a versatile tool for representing moving fronts in a
variety of physical processes, involving flow phenomena, crystal growth and phase changes
among others. The use level set methods for inverse problem in EIT received little attention
so far. The combination level set formulation to describe the shapes of the domains with
essentially nonoscilatory schemes to solve the Hamilton-Jacobi equation is efficient method
for wide class of problems involving partial differential equation.
In the full paper we are going to present experiments indicated efficiency of
combination level set method with BEM to the solution forward and inverse problem in EIT.
References
1. Aliabadi M.H., The Boundary Element Method, Volume 2, John Wiley &Sons, LTD, 2002
2. Berowski P., Stasiak M., Kwiatkowska A., Sikora J., Level Set Method and Material Derivative Concept in
Optimal Shape Design, XIV International Symposium on Theoretical Electrical Engineering, Szczecin,
Poland, 2007
3. Bertsekas D.P., Nedic A, Ozdaglar A.E., Convex Analysis and Optimization, Athena Scientific, Belmont,
2003
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