  PhaseLift, proposed by E.J. Cand\`{e}s et al., is one convex relaxation
approach for phase retrieval. The relaxation enlarges the solution set from
rank one matrices to positive semidefinite matrices.
  In this paper, a relaxation is employed to nonconvex alternating minimization
methods to recover the rank-one matrices.
  A generic measurement matrix can be standardized to a matrix consisting of
orthonormal columns. To recover the rank-one matrix, the standardized frames
are used to select the matrix with the maximal leading eigenvalue among the
rank-$r$ matrices. Empirical studies are conducted to validate the
effectiveness of this relaxation approach. In the case of Gaussian random
matrices with a sufficient number of nearly orthogonal sensing vectors, we show
that the singular vector corresponding to the least singular value is close to
the unknown signal, and thus it can be a good initialization for the nonconvex
minimization algorithm.
