  Scatterers in a homogeneous medium are imaged by probing the medium with two
point sources of waves modulated by correlated signals and by measuring only
intensities at one single receiver. For appropriately chosen source pairs, we
show that full waveform array measurements can be recovered from such intensity
measurements by solving a linear least squares problem. The least squares
solution can be used to image with Kirchhoff migration, even if the solution is
determined only up to a known one-dimensional nullspace. The same imaging
strategy can be used when the medium is probed with point sources driven by
correlated Gaussian processes and autocorrelations are measured at a single
location. Since autocorrelations are robust to noise, this can be used for
imaging when the probing wave is drowned in background noise.
