Signal to Noise Ratio Analysis in Virtual Source Array Imaging

We consider correlation-based imaging of a reflector located on one side of a passive array where the medium is homogeneous. On the other side of the array the illumination by remote impulsive sources goes through a strongly scattering medium. It has been shown in [J. Garnier and G. Papanicolaou, Inverse Problems, 28 (2012), 075002] that migrating the cross correlations of the passive array gives an image whose resolution is as good as if the array was active and the array response matrix was that of a homogeneous medium. In this paper we study the signal to noise ratio (SNR) of the image as a function of statistical properties of the strongly scattering medium, the signal bandwidth, and the source and passive receiver array characteristics. Using a Kronecker model for the strongly scattering medium we show that image resolution is as expected and that the SNR can be computed in an essentially explicit way. We show with direct numerical simulations using full wave propagation solvers in random media that the theoretical predictions based on the Kronecker model are accurate.