CALDERON CAVITIES INVERSE PROBLEM AS A SHAPE-FROM-MOMENTS PROBLEM

In this paper, we address a particular case of Calderon'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 the so-called Generalized Polia-Szego tensors (GPST) of the cavities from the DtN of the cavities. Secondly, we show that the obtained shape from the 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.