Laplace random vectors, Gaussian noise, and the generalized incomplete gamma function

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

Abstract

Wavelet domain statistical modeling of images has focused on modeling the peaked heavy-tailed behavior of the marginal distribution and on modeling the dependencies between coefficients that are adjacent (in location and/or scale). In this paper we describe the extension of the Laplace marginal model to the multivariate case so that groups of wavelet coefficients can be modeled together using Laplace marginal models. We derive the nonlinear MAP and MMSE shrinkage functions for a Laplace vector in Gaussian noise and provide computationally efficient approximations to them. The development depends on the generalized incomplete Gamma function.

Original languageEnglish (US)
Title of host publication2006 IEEE International Conference on Image Processing, ICIP 2006 - Proceedings
Pages2097-2100
Number of pages4
DOIs
StatePublished - 2006
Event2006 IEEE International Conference on Image Processing, ICIP 2006 - Atlanta, GA, United States
Duration: Oct 8 2006Oct 11 2006

Other

Other2006 IEEE International Conference on Image Processing, ICIP 2006
CountryUnited States
CityAtlanta, GA
Period10/8/0610/11/06

Keywords

  • Estimation
  • Exponential distributions
  • Image restoration
  • MAP estimation
  • Wavelet transforms

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Signal Processing

Cite this

Selesnick, I. (2006). Laplace random vectors, Gaussian noise, and the generalized incomplete gamma function. In 2006 IEEE International Conference on Image Processing, ICIP 2006 - Proceedings (pp. 2097-2100). [4106975] https://doi.org/10.1109/ICIP.2006.312821

Laplace random vectors, Gaussian noise, and the generalized incomplete gamma function. / Selesnick, Ivan.

2006 IEEE International Conference on Image Processing, ICIP 2006 - Proceedings. 2006. p. 2097-2100 4106975.

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

Selesnick, I 2006, Laplace random vectors, Gaussian noise, and the generalized incomplete gamma function. in 2006 IEEE International Conference on Image Processing, ICIP 2006 - Proceedings., 4106975, pp. 2097-2100, 2006 IEEE International Conference on Image Processing, ICIP 2006, Atlanta, GA, United States, 10/8/06. https://doi.org/10.1109/ICIP.2006.312821
Selesnick I. Laplace random vectors, Gaussian noise, and the generalized incomplete gamma function. In 2006 IEEE International Conference on Image Processing, ICIP 2006 - Proceedings. 2006. p. 2097-2100. 4106975 https://doi.org/10.1109/ICIP.2006.312821
Selesnick, Ivan. / Laplace random vectors, Gaussian noise, and the generalized incomplete gamma function. 2006 IEEE International Conference on Image Processing, ICIP 2006 - Proceedings. 2006. pp. 2097-2100
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