  An outlier-resistance phase retrieval algorithm based on alternating
direction method of multipliers (ADMM) is devised in this letter. Instead of
the widely used least squares criterion that is only optimal for Gaussian noise
environment, we adopt the least absolute deviation criterion to enhance the
robustness against outliers. Considering both intensity- and amplitude-based
observation models, the framework of ADMM is developed to solve the resulting
non-differentiable optimization problems. It is demonstrated that the core
subproblem of ADMM is the proximity operator of the L1-norm, which can be
computed efficiently by soft-thresholding in each iteration. Simulation results
are provided to validate the accuracy and efficiency of the proposed approach
compared to the existing schemes.
