Generalized wirtinger flow for passive polarimetrie reconstruction of extended dipole targets

Generalized phase retrieval problem has become a significant topic of interest in the signal processing community in recent years. Overall, non-convexity of the problem, strong assumptions regarding unknowns or computational requirements of convex relaxations have proved a non-heuristic approach to phase retrieval a challenging task. In [1], Wirtinger Flow was proposed as a non-convex approach while establishing convergence to a global optimum under certain conditions, which offered considerable advantages due to lower storage and computational requirements over lifting based counterparts. Under the observation that generalized phase retrieval is a special case of cross correlated measurement model, we consider phase retrieval literature and Wirtinger Flow method for passive imaging from interferometric measurements. We consider the polarimetric imaging problem for a distributed array of antennas, in which scene reflectivities and polarization states of stationary targets have to be simultenously reconstructed. Linear measurements collected from each antenna is correlated with the others to yield a quadratic measurement model. We then pursue the non-convex approach rather than the previously explored LRMR method, and derive Generalized Wirtinger Flow for cross correlation measurements. We present reconstruction results in comparison to LRMR method with respect to contrast, and report improved performance in identical number of computations.