  Robustness to noise and outliers is a desirable trait in phase retrieval
algorithms for many applications in imaging and signal processing. In this
paper, we develop novel robust phase retrieval algorithms based on the
minimization of reverse Kullback-Leibler divergence (RKLD) within the Wirtinger
Flow (WF) framework. We use RKLD over intensity-only measurements in two
distinct ways: i) to design a novel initial estimate based on minimum
distortion design of spectral estimates, and ii) as a loss function for
iterative refinement based on WF. The RKLD-based loss function offers implicit
regularization by processing data at the logarithmic scale and provides the
following benefits: suppressing the influence of outliers and promoting
projections orthogonal to noise subspace. We perform a quantitative analysis
demonstrating the robustness of RKLD-based minimization as compared to that of
the $\ell_2$ and Poisson loss-based minimization. We present three algorithms
based on RKLD minimization, including two with truncation schemes to enhance
the robustness to significant contamination. Our numerical study uses data
generated based on synthetic coded diffraction patterns and real optical
imaging data. The results demonstrate the advantages of our algorithms in terms
of sample efficiency, convergence speed, and robustness with respect to
outliers over the state-of-the-art techniques.
