Anisotropic Nonlocal Means Denoising
  It has recently been proved that the popular nonlocal means (NLM) denoising algorithm does not optimally denoise images with sharp edges. Its weakness lies in the isotropic nature of the neighborhoods it uses to set its smoothing weights. In response, in this paper we introduce several theoretical and practical anisotropic nonlocal means (ANLM) algorithms and prove that they are near minimax optimal for edge-dominated images from the Horizon class. On real-world test images, an ANLM algorithm that adapts to the underlying image gradients outperforms NLM by a significant margin. 
Arian Maleki, Manjari Narayan, Richard G. Baraniuk
math.ST cs.IT math.IT stat.TH