Chrysoula Tsogka, University of Crete
This talk concerns the problem of active array imaging of weak localized scatterers in randomly inhomogeneous media when only intensities are measured. To image we propose a methodology based on cross-correlations, which can be obtained from multiple-frequency intensity only measurements. The cross-correlations are the elements of the time reversal matrix for one receiver and multiple sources emitting at multiple stepped frequencies. We show how the time-reversal matrix can be obtained from intensity only measurements using an appropriate illumination strategy and the polarization identity. Imaging is based on back-propagating the elements of the time reversal matrix that correspond to cross-correlations at nearby frequencies and for nearby sources. A simple linear algebra implementation of the thresholding operation is implemented using a mask, that is a matrix with only zero and one elements. The robustness of our approach is illustrated with several numerical simulations carried out in an optical imaging regime.