Estimation Risk of Transformation-Averaged Estimators

Juan Liu, Pierre Moulin

Research output: Contribution to journalConference articlepeer-review


Wavelet image denoising practice has shown that the performance of simple estimators may be substantially improved by averaging these estimators over a collection of transformations such as translations or rotations. In this paper, we explain and quantify these empirical findings using estimation theory. We consider a general nonlinear observation model, analyze the estimation risk of transformation-averaged estimators, and derive an upper bound on the risk reduction due to transformation averaging. The bound is evaluated for several estimators, using different averaging strategies (including a randomized strategy) and different wavelet bases. The practical usefulness of the bound is established for standard image denoising examples.

Original languageEnglish (US)
Pages (from-to)87-96
Number of pages10
JournalProceedings of SPIE - The International Society for Optical Engineering
Issue number1
StatePublished - 2003
EventWavelets: Applications in Signal and Image Processing X - San Diego, CA, United States
Duration: Aug 4 2003Aug 8 2003


  • Estimation risk
  • Invariance
  • Transformation groups
  • Wavelets

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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