Target Identification Using Dictionary Matching of Generalized Polarization Tensors

The aim of this paper is to provide a fast and efficient procedure for (real-time) target identification in imaging based on matching on a dictionary of precomputed generalized polarization tensors (GPTs). The approach is based on some important properties of the GPTs and new invariants. A new shape representation is given and numerically tested in the presence of measurement noise. The stability and resolution of the proposed identification algorithm is numerically quantified.Comment: Keywords: generalized polarization tensors, target identification, shape representation, stability analysis. Submitted to Foundations of Computational Mathematic

Electrocommunication for weakly electric fish

This paper addresses the problem of the electro-communication for weakly electric fish. In particular we aim at sheding light on how the fish circumvent the jamming issue for both electro-communication and active electro-sensing. A real-time tracking algorithm is presented

Reconstruction of domains with algebraic boundaries from generalized polarization tensors

This paper aims at showing the stability of the recovery of a smooth planar domain with a real algebraic boundary from a finite number of its generalized polarization tensors. It is a follow-up of the work [H. Ammari et al., Math. Annalen, 2018], where it is proved that the minimal polynomial with real coefficients vanishing on the boundary can be identified as the generator of a one dimensional kernel of a matrix whose entries are obtained from a finite number of generalized polarization tensors. The recovery procedure is implemented without any assumption on the regularity of the domain to be reconstructed and its performance and limitations are illustrated