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 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 signal to noise ratio 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