Multivariate Statistical Models for Image Denoising in the Wavelet Domain

  • Authors:

  • Shan Tan;Licheng Jiao

  • Affiliations:

  • Institute of Intelligent Information Processing, Xidian University, Xi'an, China;Institute of Intelligent Information Processing, Xidian University, Xi'an, China

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 2007

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Abstract

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.