Imaging Using Transport Models for Wave-wave Correlations

We consider the imaging of objects buried in unknown heterogeneous media. The medium is probed by using classical (e.g., acoustic or electromagnetic) waves. When heterogeneities in the medium become too strong, inversion methodologies based on a microscopic description of wave propagation (e.g., a wave equation or Maxwell’s equations) become strongly dependent on the unknown details of the heterogeneous medium. In some situations, it is preferable to use a macroscopic model for a quantity that is quadratic in the wave fields. Here, such macroscopic models take the form of radiative transfer equations also referred to as transport equations. They can model either the energy density of the propagating wave fields or more generally the correlation of two wave fields propagating in possibly different media. In particular, we consider the correlation of the two fields propagating in the heterogeneous medium when the inclusion is absent and present, respectively. We present theoretical and numerical results showing that reconstructions based on this correlation are more accurate than reconstructions based on measurements of the energy density. Random media; Imaging; Radiative transfer AMS Subject Classification: 22E46, 53C35, 57S20