Signal restoration with overcomplete wavelet transforms

Comparison of analysis and synthesis priors

Ivan 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
Volume7446
DOIs
StatePublished - 2009
EventWavelets XIII - San Diego, CA, United States
Duration: Aug 2 2009Aug 4 2009

Other

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

Fingerprint

Restoration
wavelet analysis
restoration
Wavelet transforms
Wavelet Transform
Synthesis
Transform
synthesis
Regularization
Term
Deconvolution
norms
Cost functions
Orthonormal
Variational Approach
Denoising
Weighted Sums
Fidelity
costs
Cost Function

Keywords

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

ASJC Scopus subject areas

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

Cite this

Signal restoration with overcomplete wavelet transforms : Comparison of analysis and synthesis priors. / Selesnick, Ivan; Figueiredo, Mário A T.

Wavelets XIII. Vol. 7446 2009. 74460D.

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

Selesnick, I & Figueiredo, MAT 2009, Signal restoration with overcomplete wavelet transforms: Comparison of analysis and synthesis priors. in Wavelets XIII. vol. 7446, 74460D, Wavelets XIII, San Diego, CA, United States, 8/2/09. https://doi.org/10.1117/12.826663
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