Asymptotic Performance of Global Denoising

We provide an upper bound on the rate of convergence of the mean-squared error for global image denoising, and illustrate that this upper bound decays with increasing image size. Hence, global denoising is asymptotically optimal. At least in an oracle scenario this property does not hold for patch-based methods such as BM3D, thereby limiting their performance for large images. As observed in practice and shown in this work, this gap in performance is small for moderate size images, but it can grow quickly with image size.