## 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.