Microwave Imaging by Elastic Deformation

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 ∇·(a∇ u)+k²qu=0 in Ω, u=φ on ∂Ω, and to reliably reconstruct both the real-valued functions a and q from the internal energies a|∇ u|² and q|u|².