In this work, we revisit the global denoising framework recently introduced by Talebi & Milanfar, with the classical formalism of diagonal estimation. We analyze the asymptotic behavior of its mean-squared error restoration performance when the image size tends to infinity. We introduce precise conditions both on the image and the global filter to ensure and quantify this convergence. We also discuss open issues concerning the most challenging aspect, namely the extension of these results to the non-oracle case.