Transport-Based Imaging in Random Media

This paper derives a radiative transfer equation from first principles to model the energy density of (mono-frequency) high frequency waves propagating in a random medium composed of localized scatterers. The correlation length of the random scatterers is small compared to the overall distance of propagation so that ensemble averaging may take place. The paper also considers the detection and imaging of inclusions buried in highly scattering random media. In such multiple scattering environments, the coherent wave fields may be too weak to be used for imaging purposes. We thus propose to model the inclusions as parameters in the macroscopic radiative transfer equations and consider the imaging problem as an inverse transport problem. Numerical simulations address the domain of validity of the radiative transfer equation and of the imaging method. Wave propagation is solved by using a Foldy-Lax framework and the forward and inverse transport problems are solved by using a Monte Carlo method. Since the inverse transport problem is ill-posed, the buried inclusions are parameterized by a small number of degrees of freedom, typically their position and a few geometric properties.