Information-theoretic interpretation of Besov spaces

Hyeokho Choi, Richard Baraniuk

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

1 Scopus citations

Abstract

Besov spaces classify signals and images through the Besov norm, which is based on a deterministic smoothness measurement. Recently, we revealed the relationship between the Besov norm and the likelihood of an independent generalized Gaussian wavelet probabilistic model. In this paper, we extend this result by providing an information-theoretic interpretation of the Besov norm as the Shannon codelength for signal compression under this probabilistic mode. This perspective unites several seemingly disparate signal/image processing methods, including denoising by Besov norm regularization, complexity regularized denoising, minimum description length (MDL) processing, and maximum smoothness interpolation. By extending the wavelet probabilistic model (to a locally adapted Gaussian model), we broaden the notion of smoothness space to more closely characterize real-world data. The locally Gaussian model leads directly to a powerful wavelet-domain Wiener filtering algorithm for denoising.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
Pages675-685
Number of pages11
Volume4119
DOIs
StatePublished - 2000
EventWavelet Applications in Signal and Image Processing VIII - San Diego, CA, USA
Duration: Jul 31 2000Aug 4 2000

Other

OtherWavelet Applications in Signal and Image Processing VIII
CitySan Diego, CA, USA
Period7/31/008/4/00

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics

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