Local bivariate cauchy distribution for video denoising in 3-D complex wavelet domain

Hossein Rabbani, Mansur Vafadust, Ivan Selesnick

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


In this paper, we present a new video denoising algorithm using bivariate Cauchy probability density function (pdf) with local scaling factor for distribution of wavelet coefficients in each subband. The bivariate pdf takes into account the statistical dependency among wavelet coefficients and the local scaling factor model the empirically observed correlation between the coefficient amplitudes. Using maximum a posteriori (MAP) estimator and minimum mean squared estimator (MMSE), we describe two methods for video denoising which rely on the bivariate Cauchy random variables with high local correlation. Because separate 3-D transforms, such as ordinary 3-D wavelet transforms (DWT), have artifacts that degrade their performance for denoising, we implement our algorithms in 3-D complex wavelet transform (DCWT) domain. In addition, we use our denoising algorithm in 2-D DCWT domain, where the 2-D transform is applied to each frame individually. The simulation results show that our denoising algorithms achieve better performance than several published methods both visually and in terms of peak signal-to-noise ratio (PSNR).

Original languageEnglish (US)
Title of host publicationApplications of Digital Image Processing XXX
StatePublished - 2007
EventApplications of Digital Image Processing XXX - San Diego, CA, United States
Duration: Aug 28 2007Aug 30 2007

Publication series

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


OtherApplications of Digital Image Processing XXX
Country/TerritoryUnited States
CitySan Diego, CA


  • 3-D complex wavelet transform
  • MAP estimator
  • MMSE estimator
  • Statistical modeling

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


Dive into the research topics of 'Local bivariate cauchy distribution for video denoising in 3-D complex wavelet domain'. Together they form a unique fingerprint.

Cite this