  In the phase retrieval problem, an unknown vector is to be recovered given
quadratic measurements. This problem has received considerable attention in
recent times. In this paper, we present an algorithm to solve a nonconvex
formulation of the phase retrieval problem, that we call $\textit{Incremental
Truncated Wirtinger Flow}$. Given random Gaussian sensing vectors, we prove
that it converges linearly to the solution, with an optimal sample complexity.
We also provide stability guarantees of the algorithm under noisy measurements.
Performance and comparisons with existing algorithms are illustrated via
numerical experiments on simulated and real data, with both random and
structured sensing vectors.
