Inexact alternating optimization for phase retrieval with outliers

Most of the available phase retrieval algorithms were explicitly or implicitly developed under a Gaussian noise model, using least squares (LS) formulations. However, in some applications of phase retrieval, an unknown subset of the measurements can be seriously corrupted by outliers, where LS is not robust and will degrade the estimation performance severely. This paper presents an Alternating Iterative Reweighted Least Squares (AIRLS) method for phase retrieval in the presence of such outliers. The AIRLS employs two-block alternating optimization to retrieve the signal through solving an ℓ_p-norm minimization problem, where 0 < p < 2. The Cramér-Rao bound (CRB) for Laplacian as well as Gaussian noise is derived for the measurement model considered, and simulations show that the proposed approach outperforms state-of-the-art algorithms in heavy-tailed noise.