  Fourier phase retrieval is a classical problem that deals with the recovery
of an image from the amplitude measurements of its Fourier coefficients.
Conventional methods solve this problem via iterative (alternating)
minimization by leveraging some prior knowledge about the structure of the
unknown image. The inherent ambiguities about shift and flip in the Fourier
measurements make this problem especially difficult; and most of the existing
methods use several random restarts with different permutations. In this paper,
we assume that a known (learned) reference is added to the signal before
capturing the Fourier amplitude measurements. Our method is inspired by the
principle of adding a reference signal in holography. To recover the signal, we
implement an iterative phase retrieval method as an unrolled network. Then we
use back propagation to learn the reference that provides us the best
reconstruction for a fixed number of phase retrieval iterations. We performed a
number of simulations on a variety of datasets under different conditions and
found that our proposed method for phase retrieval via unrolled network and
learned reference provides near-perfect recovery at fixed (small) computational
cost. We compared our method with standard Fourier phase retrieval methods and
observed significant performance enhancement using the learned reference.
