Modified repeated median filters

Authors:
T. Bernholt;R. Fried;U. Gather;I. Wegener
Affiliations:
Department of Computer Science, University of Dortmund, Dortmund, Germany 44221;Department of Statistics, University Carlos III de Madrid, Getafe, Spain 28903;Department of Statistics, University of Dortmund, Dortmund, Germany 44221;Department of Computer Science, University of Dortmund, Dortmund, Germany 44221
Venue:
Statistics and Computing
Year:
2006

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Abstract

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.