  Coherent X-ray diffraction imaging (CXDI) experiments are intrinsically
limited by shot noise, a lack of prior knowledge about the sample's support,
and missing measurements due to the experimental geometry. We propose a
flexible, iterative phase retrieval framework that allows for accurate modeling
of Gaussian or Poissonian noise statistics, modified support updates,
regularization of reconstructed signals, and handling of missing data in the
observations. The proposed method is efficiently solved using alternating
direction method of multipliers (ADMM) and is demonstrated to consistently
outperform state-of-the-art algorithms for low-photon phase retrieval from CXDI
experiments, both for simulated diffraction patterns and for experimental
measurements.
