Anisotropic nonlocal means denoising

Arian Maleki, Manjari Narayan, Richard G. Baraniuk

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)452-482
Number of pages31
JournalApplied and Computational Harmonic Analysis
Issue number3
StatePublished - Nov 2013


  • Anisotropy
  • Denoising
  • Minimax risk
  • Nonlocal means

ASJC Scopus subject areas

  • Applied Mathematics


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