A ne Order { Statistic Filters : \ Medianization " of Linear FIRFilters 1
نویسندگان
چکیده
This paper introduces a novel, data{adaptive ltering framework: aane order{statistic lters. AAne order{statistic lters operate eeectively on a wide range of signal statistics, are sensitive to the dispersion of the observed data, and are therefore particularly useful in the processing of nonstationary signals. These properties result from the introduction of a tunable aanity function that measures the aanity, or closeness, of observation samples in their natural order to their corresponding order{statistics. The obtained aanity measures are utilized to control the innuence of individual samples in the ltering process. Depending on the spread of the aanity function, which is controlled by a single parameter , aane order{statistic lters operate eeectively in various environments ranging from Gaussian to impulsive. The class of aane order{statistic lters subsumes the family of weighted order{ statistic (WOS) aane lters and the class of FIR aane lters. In this paper we focus on a representative of the WOS aane lter class, the median aane lter, whose behavior can be tuned from that of a linear FIR lter to that of a robust median lter by narrowing the aanity function-a process referred to as medianization. The superior performance of aane order{statistic lters is demonstrated in two applications. 1 The aanity function A ;; assigns a low or high aanity to the sample x i depending on the location and dispersion parameters 3 (a) Gaussian probability density function and aanity function for = 0:1; 1, and 10. (b) PrfA i g for = 0:1; 1; 4 Probability that the i th order{statistic is weighted by A (i) for i=1 and 9 ({), i=2 and 8 (-), i=3 and 7 (and and i=4 and 6 (), for = 0:1 (a), = 1:0 (b), and = 10 5 subsets of (a) original and noisy image, (b) ISAR image of B-727. : : : : : : : 20 6 (a) MSE learning curves: (1) joint optimization of and w (i) 's ({), (2) optimization of only (-), (3) optimization of w (i) 's only (), where o and denote the original and the simpliied algorithms, respectively; (b) trajectories of parameter during joint optimization: original algorithm ({) and simpliied algorithm 7 (a) The noise-corrupted chirp, (b) the result of the linear FIR bandpass, (c) the FIR-WOS, (d) the L`, (e) the median aane lters, respectively, and (f) the desired 8 Feature enhancing: (a) WOS-lter, (b) absolute diierence between original and WOS-lter, (c) …
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