Multivariate Priors and the Linearity of Optimal Bayesian Estimators under Gaussian Noise

Leighton P. Barnes, Alex Dytso, Jingbo Liu +1

Consider the task of estimating a random vector $X$ from noisy observations $Y=X+Z$, where $Z$ is a standard normal vector, under the $L^p$ fidelity criterion. This work establ…