Modeling statistical properties of wavelets using a mixture of bivariate cauchy models and its application for image denoising in complex wavelet domain

Hossein Rabbani, Mansur Vafadust, Ivan Selesnick

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

Abstract

In this paper, we design a bivariate maximum a posteriori (MAP) estimator that supposes the prior of wavelet coefficients as a mixture of bivariate Cauchy distributions. This model not only is a mixture but is also bivariate. Since mixture models are able to capture the heavy-tailed property of wavelets and bivaraite distributions can model the intrascale dependences of wavelet coefficients, this bivariate mixture probability density function (pdf) can better capture statistical properties of wavelet coefficients. The simulation results show that our proposed technique achieves better performance than other methods employing non mixture pdfs such as bivariate Cauchy pdf and circular symmetric Laplacian pdf visually and in terms of peak signal-to-noise ratio (PSNR). We also compare our algorithm with several recently published denoising methods and see that it is among the best reported in the literature.

Original languageEnglish (US)
Title of host publicationWavelets XII
DOIs
StatePublished - 2007
EventWavelets XII - San Diego, CA, United States
Duration: Aug 26 2007Aug 29 2007

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume6701
ISSN (Print)0277-786X

Other

OtherWavelets XII
CountryUnited States
CitySan Diego, CA
Period8/26/078/29/07

Keywords

  • Bivariate cauchy distribution
  • Complex wavelet transform
  • MAP estimator
  • Mixture model

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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  • Cite this

    Rabbani, H., Vafadust, M., & Selesnick, I. (2007). Modeling statistical properties of wavelets using a mixture of bivariate cauchy models and its application for image denoising in complex wavelet domain. In Wavelets XII [67012I] (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 6701). https://doi.org/10.1117/12.739253