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}
}
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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.
