  We consider a popular nonsmooth formulation of the real phase retrieval
problem. We show that under standard statistical assumptions, a simple
subgradient method converges linearly when initialized within a constant
relative distance of an optimal solution. Seeking to understand the
distribution of the stationary points of the problem, we complete the paper by
proving that as the number of Gaussian measurements increases, the stationary
points converge to a codimension two set, at a controlled rate. Experiments on
image recovery problems illustrate the developed algorithm and theory.
