Perturbative numeric approach in microwave imaging

Abstract

In this article, we show that using measurements for different frequencies, and ultrasound localized perturbations it is possible to extend the method of the imaging by elastic deformation developed by Ammari et al. [H. Ammari, E. Bonnetier, Y. Capdeboscq, M. Tanter, and M. Fink, Electrical impedance tomography by elastic deformation, SIAM J. Appl. Math. 68(6) (2008), pp. 1557–1573] to problems of the form

and to reconstruct both γ and q by a perturbation method, provided that γ is coercive and k is not a resonant frequency.

Keywords:

• imaging
• Helmholtz equation
• perturbations
• inverse problem
• asymptotic analysis

AMS Subject Classifications::

• 31B20
• 31A25