Time reversal for inclusion detection in one-dimensional randomly layered media

In this work we discuss detection of changes in a random medium when the measurements are not perfect, i.e. noise from the electronic devices is included. We study a regime in which the typical length scales involved are well-separated. Moreover, since detection procedures based on the analysis of the reflected signals can fail because of the lack of coherency, we introduce a technique based on time reversal which can take advantage of both the coherent time-reversed signal and incoherency associated with the measurement noise. We use asymptotic analysis of time-reversed signals in a changing medium to guide us in the selection of a statistical decision technique. The proposed technique is illustrated by a series of numerical simulations. The results show a remarkable agreement with the asymptotic analysis and also highlight the robustness of this technique.