  We consider the recovery of a low rank $M \times N$ matrix $S$ from its noisy
observation $\tilde{S}$ in two different regimes. Under the assumption that $M$
is comparable to $N$, we propose two consistent estimators for $S$. Our
analysis relies on the local behavior of the large dimensional rectangular
matrices with finite rank perturbation. We also derive the convergent limits
and rates for the singular values and vectors of such matrices.
