High dimensional deformed rectangular matrices with applications in matrix denoising

Abstract

We consider the recovery of a low rank $M\times N$ matrix $S$ from its noisy observation $\tilde{S}$ in the high dimensional framework when $M$ is comparable to $N$. We propose two efficient estimators for $S$ under two different regimes. Our analysis relies on the local asymptotics of the eigenstructure of large dimensional rectangular matrices with finite rank perturbation. We derive the convergent limits and rates for the singular values and vectors for such matrices.