Robust Phase Retrieval via ADMM with Outliers
This work addresses outlier resistance in phase retrieval, which is important for signal processing applications, but it is incremental as it adapts existing methods to a specific noise model.
The authors tackled the problem of phase retrieval in the presence of outliers by developing an ADMM-based algorithm using the least absolute deviation criterion instead of least squares, resulting in improved robustness as validated by simulations.
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.