Modified repeated median filters

被引:28
作者
Bernholt, T
Fried, R [1 ]
Gather, U
Wegener, I
机构
[1] Univ Carlos III Madrid, Dept Stat, Getafe 28903, Spain
[2] Univ Dortmund, Dept Comp Sci, D-44221 Dortmund, Germany
[3] Univ Dortmund, Dept Stat, D-44221 Dortmund, Germany
关键词
signal extraction; robust filtering; drifts; jumps; outliers; computational geometry; update algorithm;
D O I
10.1007/s11222-006-8449-1
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
We discuss moving window techniques for fast extraction of a signal composed of monotonic trends and abrupt shifts from a noisy time series with irrelevant spikes. Running medians remove spikes and preserve shifts, but they deteriorate in trend periods. Modified trimmed mean filters use a robust scale estimate such as the median absolute deviation about the median (MAD) to select an adaptive amount of trimming. Application of robust regression, particularly of the repeated median, has been suggested for improving upon the median in trend periods. We combine these ideas and construct modified filters based on the repeated median offering better shift preservation. All these filters are compared w.r.t. fundamental analytical properties and in basic data situations. An algorithm for the update of the MAD running in time O(log n) for window width n is presented as well.
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页码:177 / 192
页数:16
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