Signal restoration with overcomplete wavelet transforms: Comparison of analysis and synthesis priors

Ivan W. Selesnick, Mário A.T. Figueiredo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The variational approach to signal restoration calls for the minimization of a cost function that is the sum of a data fidelity term and a regularization term, the latter term constituting a 'prior'. A synthesis prior represents the sought signal as a weighted sum of 'atoms'. On the other hand, an analysis prior models the coefficients obtained by applying the forward transform to the signal. For orthonormal transforms, the synthesis prior and analysis prior are equivalent; however, for overcomplete transforms the two formulations are different. We compare analysis and synthesis 1-norm regularization with overcomplete transforms for denoising and deconvolution.

Original languageEnglish (US)
Title of host publicationWavelets XIII
DOIs
StatePublished - 2009
EventWavelets XIII - San Diego, CA, United States
Duration: Aug 2 2009Aug 4 2009

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume7446
ISSN (Print)0277-786X

Other

OtherWavelets XIII
CountryUnited States
CitySan Diego, CA
Period8/2/098/4/09

Keywords

  • Deconvolution
  • Denoising
  • Signal restoration
  • Sparsity
  • Total variation
  • 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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