Calder\'on cavities inverse problem as a shape-from-moments problem
Abstract
In this paper, we address a particular case of Calder\'on'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 P\'olia-Szeg\"o 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.
Keywords
Cite
@article{arxiv.1803.03519,
title = {Calder\'on cavities inverse problem as a shape-from-moments problem},
author = {Alexandre Munnier and Karim Ramdani},
journal= {arXiv preprint arXiv:1803.03519},
year = {2018}
}