Reconstruction of averaging indicators for highly heterogeneous media

We propose a new imaging algorithm capable of producing quantitative indicator functions for unknown and possibly highly oscillating media from multi-static far field measurements of scattered fields at a fixed frequency. The algorithm exploits the notion of modified transmission eigenvalues and their determination from measurements. We propose in particular the use of a new modified background obtained as the limit of a metamaterial background. It has the advantage of having a unique non zero eigenvalue, which is particularly suited for the proposed imaging procedure. We show the efficiency of this new algorithm on some two dimensional experiments and emphasise its superiority with respect to some classical approaches such as the linear sampling method.