Microwave Imaging by Elastic Deformation

Habib Ammari (1) , Yves Capdeboscq (2) , Frédéric de Gournay (3) , Faouzi Triki (4) , Anna Rozanova-Pierrat (5)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 MI - Mathematical Institute [Oxford]
3 LMV - Laboratoire de Mathématiques de Versailles
4 EDP - Equations aux Dérivées Partielles
5 MAS - Mathématiques Appliquées aux Systèmes - EA 4037

In this paper, we show that by using microwave measurements at different frequencies and ultrasound localized perturbations to create local changes in the medium it is possible to extend the method developed by Ammari et al. in [SIAM J. Appl. Math., 68 (2008), pp. 1557-1573] to problems of the form $\nabla\cdot(a\nabla u)+k^{2}qu=0$ in $\Omega$, $u=\varphi$ on $\partial\Omega$, and to reliably reconstruct both the real-valued functions $a$ and $q$ from the internal energies $a|\nabla u|^2$ and $q|u|^2$.

Keywords: hybrid imaging; expansion methods; microwave imaging; elastic perturbation; resolution enhancement; explicit inversion formula; optimal control

Domains: Mathematics [math]; Numerical Analysis [math.NA]

Habib Ammari, Yves Capdeboscq, Frédéric de Gournay, Faouzi Triki, Anna Rozanova-Pierrat. Microwave Imaging by Elastic Deformation. SIAM Journal on Applied Mathematics, 2011, 71 (6), pp.2112-2130. ⟨10.1137/110828241⟩. ⟨hal-00655840⟩