Robust Phase Retrieval With Outliers

An outlier-resistance phase retrieval algorithm based on alternating direction method of multipliers (ADMM) is devised in this paper. 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 $\ell_1$-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.