  In this paper, a reconstruction method for the spatially distributed
dielectric constant of a medium from the back scattering wave field in the
frequency domain is considered. Our approach is to propose a globally
convergent algorithm, which does not require any knowledge of a small
neighborhood of the solution of the inverse problem in advance. The
Quasi-Reversibility Method (QRM) is used in the algorithm. The convergence of
the QRM is proved via a Carleman estimate. The method is tested on both
computationally simulated and experimental data.
