Robust amplitude method with <inline-formula><tex-math id="M1">$ L_{1/2} $</tex-math></inline-formula>-regularization for compressive phase retrieval

Abstract

Compressive phase retrieval aims to recover a sparse signal from the amplitude of its linear measurements when the number of measurements required is far less than the dimension of the signal. In real applications, the measurements are often corrupted by outliers and asymmetrical distribution noise. In this paper, we introduce a novel method for compressive phase retrieval which consists of least absolute deviation loss function and an $ L_{1/2}- $regularization term. It is a nonconvex, nonsmooth, and non-Lipschitz optimization problem. We design an efficient alternating direction method of multipliers(ADMM) to solve the problem and establish its convergence. Extensive numerical experiments demonstrate that the proposed method has higher success probability when the number of measurements is relatively less and is robust to outliers, dense bounded noise as well as Laplace noise.