Suboptimality of Nonlocal Means for Images with Sharp Edges

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(-1) log (1/2+epsilon) n, for an n-pixel image with epsilon greater than 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 mimimax rate of n(-4/3).

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Document Details

Document Type
Technical Report
Publication Date
Nov 24, 2011
Accession Number
ADA557513

Entities

People

  • Arian Maleki
  • Manjari Narayan
  • Richard G. Baraniuk

Organizations

  • Rice University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Convolution
  • Electrical Engineering
  • Engineering
  • Estimators
  • Filters
  • Filtration
  • Image Processing
  • Inequalities
  • Linear Filtering
  • Notation
  • Probability
  • Random Variables
  • Risk
  • Risk Analysis
  • Standards
  • Two Dimensional

Readers

  • Electromagnetic Wave Scattering and Antenna Radiation Engineering
  • Image Processing and Computer Vision.
  • Operations Research