Imaging with power controlled source pairs

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.