Modeling and estimation of wavelet coefficients using elliptically- contoured multivariate laplace vectors

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

Abstract

In this paper, we are interested in modeling groups of wavelet coefficients using a zero-mean, ellipticallycontoured multivariate Laplace probability distribution function (pdf). Specifically, we are interested in the problem of estimating a d-point Laplace vector, s, in additive white Gaussian noise (AWGN), n, from an observation, y = s + n. In the scalar case (d = 1), the MAP and MMSE estimators are already known; and in the vector case (d > 1), the MAP estimator can be obtained by an iterative successive substitution algorithm. For the special case where the contour of the Laplace pdf is spherical, the MMSE estimators for the vector case (d > 1) have been derived in our previous work; we have shown that the MMSE estimator can be expressed in terms of the generalized incomplete Gamma function. For the general ellipticallycontoured case, the MMSE estimator can not be expressed as such. In this paper, we therefore investigate approximations to the MMSE estimator of a Laplace vector in AWGN.

Original languageEnglish (US)
Title of host publicationWavelets XII
Volume6701
DOIs
StatePublished - 2007
EventWavelets XII - San Diego, CA, United States
Duration: Aug 26 2007Aug 29 2007

Other

OtherWavelets XII
CountryUnited States
CitySan Diego, CA
Period8/26/078/29/07

Fingerprint

estimators
coefficients
Probability distributions
Distribution functions
probability distribution functions
random noise
gamma function
Substitution reactions
estimating
substitutes
scalars
approximation

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics

Cite this

Modeling and estimation of wavelet coefficients using elliptically- contoured multivariate laplace vectors. / Selesnick, Ivan.

Wavelets XII. Vol. 6701 2007. 67011K.

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

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