High dimensional deformed rectangular matrices with applications in matrix denoising

Understand

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.