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Simon Burley, University of Leeds (U.K.)
Michael Darnell, University of Leeds (U.K.)
It is widely acknowledged that the effect of impulsive noise is a major source of performance degradation within a wide range of communication systems. This is due to the fact that non-Gaussian interference is neglected within the system design philosophy for reasons of complexity and tractability. In this paper, we directly address this problem using a novel 'de-noising' technique in which significant performance gains are achieved with low-complexity.
ic973417.pdf
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Irvin C. Schick, BBN, Cambridge (U.S.A.)
Hamid Krim, MIT, Cambridge (U.S.A.)
Approaches to wavelet-based denoising (or signal enhancement) have so far relied on the assumption of normally distributed perturbations. To relax this assumption, which is often violated in practice, we derive a robust wavelet thresholding technique based on the Minimax Description Length principle. We first determine the least favorable distribution in the (varepsilon)-contaminated normal family as the member that maximizes the entropy. We show that this distribution and the best estimate based upon it, namely the Maximum Likelihood Estimate, constitute a saddle point. This results in a threshold that is more resistant to heavy-tailed noise, but for which the estimation error is still potentially unbounded. We address the practical case where the underlying signal is known to be bounded, and derive a two-sided thresholding technique that is resistant to outliers and has bounded error. We provide illustrative examples.
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Eric Moreau, ISITV (France)
Jean-Christophe Pesquet, University of Paris Sud (France)
In this work, extended forms of contrast functions are introduced to provide statistical measures of independence for orthogonal mixtures. We also define semicontrasts based on second-order statistics which, in some cases, may be sufficient to separate the mixed sources. The corresponding criteria are then used to obtain an optimized representation of a stochastic process in an orthonormal basis of wavelet packets or local cosines.
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Matthew Crouse, Rice University (U.S.A.)
Richard Baraniuk, Rice University (U.S.A.)
Robert Nowak, MSU (U.S.A.)
Current wavelet-based statistical signal and image processing techniques such as shrinkage and filtering treat the wavelet coefficients as though they were statistically independent. This assumption is unrealistic; considering the statistical dependencies between wavelet coefficients can yield substantial performance improvements. In this paper, we develop a new framework for wavelet-based signal processing that employs hidden Markov models to characterize the dependencies between wavelet coefficients. To illustrate the power of the new framework, we derive a new algorithm for signal estimation in nonGaussian noise.
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Paulo Gonçalvès, INRIA Rocquencourt (France)
Patrice Abry, CNRS URA 1325 - ENS. Lyon (France)
We propose here a multiple-window wavelet transform for the purpose of identifying non-stationary self-similar structures in random processes and estimating the time-varying scaling exponent H(t) that controls the local regularity and correlation of the process. More specifically, our final aim is to be able to track even rapidly varying trajectories (t,H(t)). The solution described here combines analysis obtained from scalograms computed with a set of multi-windows designed so as to satisfy to a decorrelation condition. We derive here the statistics for the estimate of H(t), compare it against numerical simulations and show that we obtain a substantial reduction of variance in estimation, without introducing bias.
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