Image restoration using statistical wavelet models

Juan Liu, Pierre Moulin

Research output: Contribution to journalConference articlepeer-review


In this paper, we propose an image restoration algorithm based on state-of-the-art wavelet domain statistical models. We present an efficient method to estimate the model parameters from the observations, and solve the restoration problem in orthonormal and translation-invariant (TI) wavelet domains. Substantial improvements over previous wavelet-based restoration methods are obtained. The use of a TI wavelet transform further enhances the restoration performance. We study the improvement from the viewpoint of Bayesian estimation theory and show that replacing an estimator with its TI version will reduce the expected risk if the signal and the degradation model are stationary.

Original languageEnglish (US)
Pages (from-to)20-33
Number of pages14
JournalProceedings of SPIE - The International Society for Optical Engineering
StatePublished - 2001
EventWavelets: Applications in Signal and Image Processing IX - San Diego, CA, United States
Duration: Jul 30 2001Aug 1 2001


  • Bayesian risk
  • Image restoration
  • Overcomplete wavelet representation
  • Statistical modeling

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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