Electrical impedance tomography: from topology to shape

• Autorzy: Hintermuller M. , Laurain A.
• Języki publikacji: EN

Abstrakty

EN

A level set based shape and topology optimization approach to electrical impedance tomography (EIT) problems with piecewise constant conductivities is introduced. The proposed solution algorithm is initialized by using topological sensitivity analysis. Then it relies on the notion of shape derivatives to update the shape of the domains where conductivity takes different values.

Słowa kluczowe

EN

electrical impedance tomography; inverse problem; shape derivative; topological derivative; level set method

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2008
• Tom: Vol. 37, no 4
• Strony: 913--933
• Opis fizyczny: Bibliogr. 11 poz., wykr.

Twórcy

autor

Hintermuller M.

autor

Laurain A.

• Department of Mathematics, University of Sussex Palmer, Brighton, UK

Bibliografia

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• BORCEA, L. (2002) Electrical Impedance Tomography. Inverse Problems 18, R99-R136.
• BRÜHL, M., HANKE, M. and VOGELIUS, M. (2003) A direct impedance tomography algorithm for locating small inhomogeneities. Numer. Math. 93, 635-654.
• CEDIO-FENGYA, D.J., MOSKOW, S. and VOGELIUS, M.S. (1998) Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction. Inverse Problems 14, 553-595.
• CHENEY, M., ISAACSON, D. and NEWELL, J.C. (1999) Electrical impedance tomography. SIAM Rev. 41, 85-101.
• CHUNG, E.T., CHAN, T.F. AND TAI, X.C. (2005) Electrical Impedance Tomography Using Level Set Representation and Total Variational Regularization. J. Comput. Phys. 205, 357-372.
• HENROT, A. and PIERRE, M. (2005) Variation et optimisation de formes: une analyse geometrique. Springer. Mathematiques et Applications 48.
• OSHER, S. and FEDKIW, R. (2003) Level Set Methods and Dynamic Implicit Surfaces. Springer, Applied Mathematical Sciences.
• OSHER, S. and SETHIAN, J. (1988) Fronts propagating with curvature-dependant speed: algorithms based on Hamilton-Jacobi formulation. J. Comp. Phys. 79, 12-49.
• SOKOŁOWSKI, J. and ŻOCHOWSKI, A. (1999) On the topological derivative in shape optimization. SIAM J. Control Optim. 37, 1251-1272.
• SOKOŁOWSKI, J. and ZOLÉSIO, J.-P. (1992) Introduction to Shape Optimization. Springer-Verlag, Computational Mathematics 16, Berlin.