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

Ivan W. Selesnick

doi:10.1109/ICIP.2006.312821

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

Ivan W. Selesnick

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	2006 IEEE International Conference on Image Processing, ICIP 2006 - Proceedings
Pages	2097-2100
Number of pages	4
DOIs	https://doi.org/10.1109/ICIP.2006.312821
State	Published - 2006
Event	2006 IEEE International Conference on Image Processing, ICIP 2006 - Atlanta, GA, United States Duration: Oct 8 2006 → Oct 11 2006

Publication series

Name	Proceedings - International Conference on Image Processing, ICIP
ISSN (Print)	1522-4880

Other

Other	2006 IEEE International Conference on Image Processing, ICIP 2006
Country/Territory	United States
City	Atlanta, GA
Period	10/8/06 → 10/11/06

Keywords

Estimation
Exponential distributions
Image restoration
MAP estimation
Wavelet transforms

ASJC Scopus subject areas

Software
Computer Vision and Pattern Recognition
Signal Processing

Access to Document

10.1109/ICIP.2006.312821

Cite this

Laplace random vectors, Gaussian noise, and the generalized incomplete gamma function. / Selesnick, Ivan W.
2006 IEEE International Conference on Image Processing, ICIP 2006 - Proceedings. 2006. p. 2097-2100 4106975 (Proceedings - International Conference on Image Processing, ICIP).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Selesnick, IW 2006, Laplace random vectors, Gaussian noise, and the generalized incomplete gamma function. in 2006 IEEE International Conference on Image Processing, ICIP 2006 - Proceedings., 4106975, Proceedings - International Conference on Image Processing, ICIP, 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

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KW - Exponential distributions

KW - Image restoration

KW - MAP estimation

KW - Wavelet transforms

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

Abstract

Publication series

Other

Keywords

ASJC Scopus subject areas

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