Advances in inverse scattering arising from the physical meaning of the Linear Sampling Method

The Linear Sampling Method (LSM) is a very effective method to image the shape of a target from the measure of the field it scatters. In this communication, we describe some results that significantly enhance the capabilities of the method, leading to new and completely original imaging strategies. First, we propose a novel strategy to image complex targets based on the use of the multipole series´ terms, that in some sense provides a generalization of the LSM and improve its performance which are indeed not as accurate when tackling this kind of targets. As a second contribution, we show that LSM can provide the basis to set an effective quantitative imaging procedure capable of retrieving not only the shape, but also the electromagnetic properties of the unknown scatterers. In particular, such a new procedure is remarkably effective as it simply involves the solution of a linear inverse problem.