Perturbative numeric approach in microwave imaging

Anna Rozanova-Pierrat (1, 2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

In this paper, we show that using measurements for different frequencies, and using ultrasound localized perturbations it is possible to extend the method of the imaging by elastic deformation developed by Ammari and al. [Electrical Impedance Tomography by Elastic Deformation SIAM J. Appl. Math. , 68(6), (2008), 1557–1573.] to problems for the Helmholtz equations with Neumann boundary conditions, and to reconstruct by a perturbation method both the conductivity and the permittivity, provided that the conductivity function is coercive and the wave number in the Helmholtz equation is not a resonant frequency.

Mots clés: imaging; Helmholtz equation; perturbations; inverse problem; asymptotic analysis

Domaines: Equations aux dérivées partielles [math.AP]

Anna Rozanova-Pierrat. Perturbative numeric approach in microwave imaging. 2009. ⟨hal-00474345⟩