  In this paper, we consider the problem of low-rank phase retrieval whose
objective is to estimate a complex low-rank matrix from magnitude-only
measurements. We propose a hierarchical prior model for low-rank phase
retrieval, in which a Gaussian-Wishart hierarchical prior is placed on the
underlying low-rank matrix to promote the low-rankness of the matrix. Based on
the proposed hierarchical model, a variational expectation-maximization (EM)
algorithm is developed. The proposed method is less sensitive to the choice of
the initialization point and works well with random initialization. Simulation
results are provided to illustrate the effectiveness of the proposed algorithm.
