  In this paper, we develop a concrete algorithm for phase retrieval, which we
refer to as Gauss-Newton algorithm. In short, this algorithm starts with a good
initial estimation, which is obtained by a modified spectral method, and then
update the iteration point by a Gauss-Newton iteration step. We prove that a
re-sampled version of this algorithm quadratically converges to the solution
for the real case with the number of random measurements being nearly minimal.
Numerical experiments also show that Gauss-Newton method has better performance
over the other algorithms.
