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Admittivity imaging from multi-frequency micro-electrical impedance tomography
Ammari, Habib,Giovangigli, Laure,Nguyen, Loc Hoang,Seo, Jin-Keun Academic Press 2017 Journal of mathematical analysis and applications Vol.449 No.2
<P><B>Abstract</B></P> <P>The aim of this paper is to propose an optimal control optimization algorithm for reconstructing admittivity distributions (i.e., both conductivity and permittivity) from multi-frequency micro-electrical impedance tomography. A convergent and stable optimal control scheme is shown to be obtainable from multi-frequency data. This opens a door for convergence analysis of optimal control type approaches in imaging from internal data. The results of this paper have potential applicability in cancer imaging, cell culturing and differentiation, food sciences, and biotechnology.</P>
Level-Set Based Shape Reconstruction Using the Generalized Polarization Tensors
Habib Ammari,Hyeonbae Kang,Josselin Garnier,Mikyoung Lim,Sanghyeon Yu 한국산업응용수학회 2011 한국산업응용수학회 학술대회 논문집 Vol.6 No.2
With each Lipschitz domain and material parameter, an infinite number of tensors, called the Generalized Polarization Tensors (GPTs), is associated. The GPTs contain significant information on the shape of the domain and its material parameter. In recent paper [5], we designed an optimization algorithm to recover fine shape details of a given domain using the GPTs by minimizing a weighted discrepancy functional. In the contained numerical experiments, the results are good, but it has the limitation that we cannot change the topology. In order to make the topology change possible, we add the level-set framework in the optimization procedure. We perform some numerical experiments to demonstrate the validity of the proposed method.