I. Introduction
In recent years there has been a large amount of work on the phase retrieval (PR) problem and on its generalization. The original PR problem involves recovering a length- signal from the magnitudes of its discrete Fourier transform (DFT) coefficients. Generalized PR replaces the DFT by inner products with any set of measurement vectors, . Thus, the goal is to recover from , . These magnitude-only measurements are referred to as phaseless measurements. PR is a classical problem that occurs in many applications such as X-ray crystallography, astronomy, and ptychography because the phase information is either difficult or impossible to obtain [3]. Algorithms for solving it have existed since the work of Gerchberg and Saxton and Fineup [4], [5]. In recent years, there has been much renewed interest in PR, e.g., [3], [6]– [18] and in sparse PR, e.g., [19] –[21].