Estimation of Laplace Random Vectors in AWGN

The estimation of spherically-contoured Laplace random vectors in additive white Gaussian noise (pdf file, 640 KB)
Ivan W. Selesnick. IEEE Trans. on Signal Processing, 56(8):3482-3496, August 2008. Preprint (pdf file, 680 KB)

ICIP 2006: Laplace Random Vectors, Gaussian Noise, and the Generalized Incomplete Gamma Function (pdf file, 344 KB)

This work develops and compares the MAP and MMSE estimators for spherically-contoured multivariate Laplace random vectors in additive white Gaussian noise (AWGN). 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 work 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.

Research supported by ONR grant N000140310217

Ivan Selesnick
Polytechnic University
Brooklyn, NY
selesi@poly.edu