International Journal of Computer Vision

, Volume 75, Issue 2, pp 209–230 | Cite as

Multivariate Statistical Models for Image Denoising in the Wavelet Domain

  • Shan Tan
  • Licheng Jiao


We model wavelet coefficients of natural images in a neighborhood using the multivariate Elliptically Contoured Distribution Family (ECDF) and discuss its application to the image denoising problem. A desirable property of the ECDF is that a multivariate Elliptically Contoured Distribution (ECD) can be deduced directly from its lower dimension marginal distribution. Using the property, we extend a bivariate model that has been used to successfully model the 2-D joint probability distribution of a two dimension random vector—a wavelet coefficient and its parent—to multivariate cases. Though our method only provides a simple and rough characterization of the full probability distribution of wavelet coefficients in a neighborhood, we find that the resulting denoising algorithm based on the extended multivariate models is computably tractable and produces state-of-the-art restoration results. In addition, we discuss the equivalence relation between our denoising algorithm and several other state-of-the-art denoising algorithms. Our work provides a unified mathematic interpretation of a type of statistical denoising algorithms. We also analyze the limitations and advantages of algorithms of this type.


natural image statistics multivariate model elliptically contoured distribution family image denoising 


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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • Shan Tan
    • 1
  • Licheng Jiao
    • 1
  1. 1.Institute of Intelligent Information ProcessingXidian UniversityXi’anChina

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