Global denoising is asymptotically optimal

In this paper an upper bound on the decay rate of the mean-squared error for global image denoising is derived. As image size increases, this upper bound decays to zero; that is, the global denoising is asymptotically optimal. Unlike patch-based methods such as BM3D, this property only holds for global denoising schemes. In practice, and as demonstrated in this work, this performance gap between patch-based and global denoisers can grow rapidly with image size.