  We consider the problem of estimation of a low-rank matrix from a limited
number of noisy rank-one projections. In particular, we propose two fast,
non-convex \emph{proper} algorithms for matrix recovery and support them with
rigorous theoretical analysis. We show that the proposed algorithms enjoy
linear convergence and that their sample complexity is independent of the
condition number of the unknown true low-rank matrix. By leveraging recent
advances in low-rank matrix approximation techniques, we show that our
algorithms achieve computational speed-ups over existing methods. Finally, we
complement our theory with some numerical experiments.
