A globally convergent numerical method for a 1-d inverse medium problem   with experimental data
  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. 
Michael V. Klibanov, Loc H. Nguyen, Anders Sullivan, and Lam Nguyen
math.AP