Suboptimality of nonlocal means for images with sharp edges

Arian Maleki, Manjari Narayan, Richard G. Baraniuk

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

We conduct an asymptotic risk analysis of the nonlocal means image denoising algorithm for the Horizon class of images that are piecewise constant with a sharp edge discontinuity. We prove that the mean square risk of an optimally tuned nonlocal means algorithm decays according to n- 1log1 /2+εn, for an n×n-pixel image with ε>0. This decay rate is an improvement over some of the predecessors of this algorithm, including the linear convolution filter, median filter, and the SUSAN filter, each of which provides a rate of only n- 2/3. It is also within a logarithmic factor from optimally tuned wavelet thresholding. However, it is still substantially lower than the optimal minimax rate of n- 4/3.

Original languageEnglish (US)
Pages (from-to)370-387
Number of pages18
JournalApplied and Computational Harmonic Analysis
Volume33
Issue number3
DOIs
StatePublished - Nov 2012

Keywords

  • Denoising
  • Horizon class
  • Linear filter
  • Minimax risk
  • Nonlocal means
  • SUSAN filter
  • Wavelet thresholding

ASJC Scopus subject areas

  • Applied Mathematics

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