NDLI: MMSE Estimation of Sparse Lévy Processes

Content Provider	IEEE Xplore Digital Library
Author	Kamilov, U. S. Pad, P. Amini, A. Unser, M.
Copyright Year	1991
Abstract	We investigate a stochastic signal-processing framework for signals with sparse derivatives, where the samples of a Lévy process are corrupted by noise. The proposed signal model covers the well-known Brownian motion and piecewise-constant Poisson process; moreover, the Lévy family also contains other interesting members exhibiting heavy-tail statistics that fulfill the requirements of compressibility. We characterize the maximum-a-posteriori probability (MAP) and minimum mean-square error (MMSE) estimators for such signals. Interestingly, some of the MAP estimators for the Lévy model coincide with popular signal-denoising algorithms (e.g., total-variation (TV) regularization). We propose a novel non-iterative implementation of the MMSE estimator based on the belief-propagation (BP) algorithm performed in the Fourier domain. Our algorithm takes advantage of the fact that the joint statistics of general Lévy processes are much easier to describe by their characteristic function, as the probability densities do not always admit closed-form expressions. We then use our new estimator as a benchmark to compare the performance of existing algorithms for the optimal recovery of gradient-sparse signals.
Sponsorship	IEEE Signal Processing Society
Starting Page	137
Ending Page	147
Page Count	11
File Size	2517526
File Format	PDF
ISSN	1053587X
Volume Number	61
Issue Number	1
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Estimation Stochastic processes Random variables Vectors Probability distribution Distortion measurement Bayesian methods total-variation estimation Belief propagation Lévy process message passing nonlinear reconstruction sparse-signal estimation stochastic modeling
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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