Wavelet statistical models and Besov spaces

Hyeokho Choi, Richard Baraniuk

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

20 Scopus citations

Abstract

We discover a new relationship between two seemingly different image modeling methodologies; the Besov space theory and the wavelet-domain statistical image models. Besov spaces characterize the set of real-world images through a deterministic characterization of the image smoothness, while statistical image models capture the probabilistic properties of images. By establishing a relationship between the Besov norm and the normalized likelihood function under an independent wavelet-domain generalized Gaussian model, we obtain a new interpretation of the Besov norm which provides a natural generalization of the theory for practical image processing. Based on this new interpretation of the Besov space, we propose a new image denoising algorithm based on projections onto the convex sets defined in the Besov space. After pointing out the limitations of Besov spaces, we propose possible generalizations using more accurate image models.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
PublisherSociety of Photo-Optical Instrumentation Engineers
Pages489-501
Number of pages13
Volume3813
StatePublished - 1999
EventProceedings of the 1999 Wavelet Applications in Signal and Image Processing VII - Denver, CO, USA
Duration: Jul 19 1999Jul 23 1999

Other

OtherProceedings of the 1999 Wavelet Applications in Signal and Image Processing VII
CityDenver, CO, USA
Period7/19/997/23/99

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics

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