Suboptimality of nonlocal means on images with sharp edges

Arian Maleki, Manjari Narayan, Richard G. Baraniuk

Abstract: We conduct an asymptotic risk analysis of the non-local means image denoising algorithm for Horizon class images that are piecewise constant with a sharp edge discontinuity. We prove that the mean-square risk of nonlocal means is suboptimal and in fact is within a log factor of the mean square risk of wavelet thresholding.