Robust Phase Retrieval via ADMM with Outliers

TL;DR

This paper introduces a robust phase retrieval algorithm using ADMM that employs the least absolute deviation criterion to effectively handle outliers, outperforming traditional least squares-based methods.

Contribution

The paper develops an ADMM-based phase retrieval method utilizing the L1-norm for enhanced outlier robustness, applicable to both intensity- and amplitude-based models.

Findings

Demonstrates improved robustness against outliers compared to existing methods.

Shows efficient computation via soft-thresholding in ADMM iterations.

Validates accuracy and efficiency through simulation results.

Abstract

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.