The linear sampling method for inhomogeneous medium and buried objects from far field measurements

We are concerned with the reconstruction of both the penetrable inhomogeneous medium and the buried impenetrable obstacle. Firstly, the classical linear sampling method is used to recover the support of the inhomogeneous medium, and then a modification of the linear sampling method is proposed for objects buried in a known layered medium. The main feature of our method is that it avoids using knowledge of the Green's function for the background media. Finally, some numerical experiments are presented to demonstrate the feasibility and effectiveness of our method.