Calderón cavities inverse problem as a shape-from-moments problem

Abstract : In this paper, we address a particular case of Calderón's (or conductivity) inverse problem in dimension two, namely the case of a homogeneous background containing a finite number of cavities (i.e. heterogeneities of infinitely high conductivities). We aim to recover the location and the shape of the cavities from the knowledge of the Dirichlet-to-Neumann (DtN) map of the problem. The proposed reconstruction method is non iterative and uses two main ingredients. First, we show how to compute so-called generalized Pólia-Szegö tensors (GPST) of the cavities from the DtN of the cavities. Secondly, we show that the obtained shape from GPST inverse problem can be transformed into a shape from moments problem, for some particular configurations. However, numerical results suggest that the reconstruction method is efficient for arbitrary geometries.
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Quarterly of Applied Mathematics, American Mathematical Society, In press, 76, pp.407-435. 〈10.1090/qam/1505〉
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Alexandre Munnier, Karim Ramdani. Calderón cavities inverse problem as a shape-from-moments problem. Quarterly of Applied Mathematics, American Mathematical Society, In press, 76, pp.407-435. 〈10.1090/qam/1505〉. 〈hal-01503425〉

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