  We consider reflector imaging in a weakly random waveguide. We address the
situation in which the source is farther from the reflector to be imaged than
the energy equipartition distance, but the receiver array is closer to the
reflector to be imaged than the energy equipartition distance. As a
consequence, the reflector is illuminated by a partially coherent field and the
signals recorded by the receiver array are noisy. This paper shows that
migration of the recorded signals cannot give a good image, but an appropriate
migration of the cross correlations of the recorded signals can give a very
good image. The resolution and stability analysis of this original functional
shows that the reflector can be localized with an accuracy of the order of the
wavelength even when the receiver array has small aperture, and that broadband
sources are necessary to ensure statistical stability, whatever the aperture of
the array.
