Precise Performance of Linear Denoisers in the Proportional Regime
arXiv:2603.18483v1 Announce Type: new Abstract: In the present paper we study the performance of linear denoisers for noisy data of the form $mathbf{x} + mathbf{z}$, where $mathbf{x} in mathbb{R}^d$ is the desired data with zero mean and unknown covariance $mathbf{Sigma}$, and $mathbf{z} sim mathcal{N}(0, mathbf{Sigma}_{mathbf{z}})$ is additive noise. Since the covariance $mathbf{Sigma}$ is not known, the standard Wiener filter cannot be employed for denoising. Instead we assume we are given samples $mathbf{x}_1,dots,mathbf{x}_n in mathbb{R}^d$ from the true distribution. […]