Statistically-Efficient Filtering in Impulsive Environments: Weighted Myriad Filters
<p/> <p>Linear filtering theory has been largely motivated by the characteristics of Gaussian signals. In the same manner, the proposed <it>Myriad Filtering</it> methods are motivated by the need for a flexible filter class with high statistical efficiency in non-Gaussian imp...
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Online Access: | http://dx.doi.org/10.1155/S1110865702000483 |
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doaj-8e1341caffdd4836ac2173241d97ca4a2020-11-25T00:32:58ZengSpringerOpenEURASIP Journal on Advances in Signal Processing1687-61721687-61802002-01-0120021363195Statistically-Efficient Filtering in Impulsive Environments: Weighted Myriad FiltersGonzalez Juan GArce Gonzalo R<p/> <p>Linear filtering theory has been largely motivated by the characteristics of Gaussian signals. In the same manner, the proposed <it>Myriad Filtering</it> methods are motivated by the need for a flexible filter class with high statistical efficiency in non-Gaussian impulsive environments that can appear in practice. Myriad filters have a solid theoretical basis, are inherently more powerful than median filters, and are very general, subsuming traditional linear FIR filters. The foundation of the proposed filtering algorithms lies in the definition of the <it>myriad</it> as a tunable estimator of location derived from the theory of robust statistics. We prove several fundamental properties of this estimator and show its optimality in practical impulsive models such as the <inline-formula><graphic file="1687-6180-2002-363195-i1.gif"/></inline-formula>-<it>stable</it> and <it>generalized</it>- <inline-formula><graphic file="1687-6180-2002-363195-i2.gif"/></inline-formula>. We then extend the myriad estimation framework to allow the use of weights. In the same way as linear FIR filters become a powerful generalization of the mean filter, filters based on running myriads reach all of their potential when a weighting scheme is utilized. We derive the "normal" equations for the optimal myriad filter, and introduce a suboptimal methodology for filter tuning and design. The strong potential of myriad filtering and estimation in impulsive environments is illustrated with several examples.</p>http://dx.doi.org/10.1155/S1110865702000483weighted myriad filtersweighted median filtersimpulsive noiseheavy tailsalpha-stable distributionsCauchy distributionphase-locked loop |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Gonzalez Juan G Arce Gonzalo R |
spellingShingle |
Gonzalez Juan G Arce Gonzalo R Statistically-Efficient Filtering in Impulsive Environments: Weighted Myriad Filters EURASIP Journal on Advances in Signal Processing weighted myriad filters weighted median filters impulsive noise heavy tails alpha-stable distributions Cauchy distribution phase-locked loop |
author_facet |
Gonzalez Juan G Arce Gonzalo R |
author_sort |
Gonzalez Juan G |
title |
Statistically-Efficient Filtering in Impulsive Environments: Weighted Myriad Filters |
title_short |
Statistically-Efficient Filtering in Impulsive Environments: Weighted Myriad Filters |
title_full |
Statistically-Efficient Filtering in Impulsive Environments: Weighted Myriad Filters |
title_fullStr |
Statistically-Efficient Filtering in Impulsive Environments: Weighted Myriad Filters |
title_full_unstemmed |
Statistically-Efficient Filtering in Impulsive Environments: Weighted Myriad Filters |
title_sort |
statistically-efficient filtering in impulsive environments: weighted myriad filters |
publisher |
SpringerOpen |
series |
EURASIP Journal on Advances in Signal Processing |
issn |
1687-6172 1687-6180 |
publishDate |
2002-01-01 |
description |
<p/> <p>Linear filtering theory has been largely motivated by the characteristics of Gaussian signals. In the same manner, the proposed <it>Myriad Filtering</it> methods are motivated by the need for a flexible filter class with high statistical efficiency in non-Gaussian impulsive environments that can appear in practice. Myriad filters have a solid theoretical basis, are inherently more powerful than median filters, and are very general, subsuming traditional linear FIR filters. The foundation of the proposed filtering algorithms lies in the definition of the <it>myriad</it> as a tunable estimator of location derived from the theory of robust statistics. We prove several fundamental properties of this estimator and show its optimality in practical impulsive models such as the <inline-formula><graphic file="1687-6180-2002-363195-i1.gif"/></inline-formula>-<it>stable</it> and <it>generalized</it>- <inline-formula><graphic file="1687-6180-2002-363195-i2.gif"/></inline-formula>. We then extend the myriad estimation framework to allow the use of weights. In the same way as linear FIR filters become a powerful generalization of the mean filter, filters based on running myriads reach all of their potential when a weighting scheme is utilized. We derive the "normal" equations for the optimal myriad filter, and introduce a suboptimal methodology for filter tuning and design. The strong potential of myriad filtering and estimation in impulsive environments is illustrated with several examples.</p> |
topic |
weighted myriad filters weighted median filters impulsive noise heavy tails alpha-stable distributions Cauchy distribution phase-locked loop |
url |
http://dx.doi.org/10.1155/S1110865702000483 |
work_keys_str_mv |
AT gonzalezjuang statisticallyefficientfilteringinimpulsiveenvironmentsweightedmyriadfilters AT arcegonzalor statisticallyefficientfilteringinimpulsiveenvironmentsweightedmyriadfilters |
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1725318016134021120 |