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 coefficents, 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 WOS affine filter 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. In this paper 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 non-stationary in nature.