Affine order statistic filters: a data-adaptive filtering framework for nonstationary signals

We introduce a novel, data-adaptive, and robust filtering framework: affine order statistic filters. Affine order statistics relate classical order statistics to observations in their natural order and thus inherently yield a meaningful data representation. Affine order statistic filters exploit this notion to adaptively process nonstationary signals. Affine order statistic filters overcome many of the limitations associated with traditional order statistic filters, in particular: filters in this class are parsimonious in the number of filter coefficients, they are statistically efficient in a wide range of signal statistics, and they admit real-valued filter weights leading to a wide-range of filtering characteristics. The class of affine order statistic filters contains two families: the weighted order statistic (WOS) affine fitter class whose structure can adapt, according to the observed data, from an FIR linear filter to a WOS filter, and the FIR affine filter class whose structure can adapt from an L-filter to an FIR-filter. We introduce the median affine filter and the center affine filter as representatives of each class, and show their performance in two applications where the signals are nonstationary in nature