Robust Phase Retrieval with Non-Convex Penalties

Abstract

This paper proposes an alternating direction method of multiplier (ADMM) based algorithm for solving the sparse robust phase retrieval with non-convex and non-smooth sparse penalties, such as minimax concave penalty (MCP). The accuracy of the robust phase retrieval, which employs an l <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> based estimator to handle outliers, can be improved in a sparse situation by adding a non-convex and non-smooth penalty function, such as MCP, which can provide sparsity with a low bias effect. This problem can be effectively solved using a novel proximal ADMM algorithm, and under mild conditions, the algorithm is shown to converge to a stationary point. Several simulation results are presented to verify the accuracy and efficiency of the proposed approach compared to existing methods.