## The Estimation of Laplace Random Vectors in AWGN and the Generalized Incomplete Gamma Function (2007)

### BibTeX

@MISC{Selesnick07theestimation,

author = {Ivan W. Selesnick},

title = {The Estimation of Laplace Random Vectors in AWGN and the Generalized Incomplete Gamma Function},

year = {2007}

}

### OpenURL

### Abstract

This paper develops and compares the MAP and MMSE estimators for spherically-contoured multivariate Laplace random vectors in additive white Gaussian noise. The MMSE estimator is expressed in closed-form using the generalized incomplete gamma function. We also find a computationally efficient yet accurate approximation for the MMSE estimator. In addition, this paper develops an expression for the mean square error MSE for any estimator of spherically-contoured multivariate Laplace random vectors in AWGN, the development of which again depends on the generalized incomplete gamma function. The estimators are motivated and tested on the problem of wavelet-based image denoising.

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Citation Context ...on with the true multivariate Laplace density to show the differences between them. It is useful to employ the true multivariate Laplace density because then Laplace models (or Laplace mixture models =-=[46]-=-) for the univariate marginal can be directly extrapolated to obtain multivariate probability models for groups of coefficients. 1.1 Empirical Histograms Fig. 2 illustrates the histogram of the coeffi... |

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Citation Context ...ficient is modeled and estimated. For example, the LAWMAP and LAWML algorithms [42] model the coefficients as Gaussian conditioned on the local variance. (Modifications of the LAWMAP are developed in =-=[8,34]-=-.) However, a non-stationary model sometimes requires that the local variance be estimated in addition to the coefficient itself, which leads to a two-layer problem. In Section 9, we write the LAWMAP ... |

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