Kinetic Models for Imaging in Random Media

Abstract

We derive kinetic models for the correlations and the energy densities of wave fields propagating in random media. These models take the form of radiative transfer and diffusion equations. We use these macroscopic models to address the detection and imaging of small objects buried in highly heterogeneous media. More specifically, we quantify the influence of small objects on (i) the energy density measured at an array of detectors and (ii) the correlation between the wave field measured in the absence of the object and the wave field measured in the presence of the object. We analyze the advantages and disadvantages of such measurements as a function of the level of disorder in the random media. Numerical simulations verify the theoretical predictions.