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

High dimensional deformed rectangular matrices with applications in matrix denoising