Affine order-statistic filters: "Medianization" of linear FIR filters

This paper introduces a novel, data-adaptive filtering framework: affine order-statistic filters. Affine order-statistic filters operate effectively 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 affinity function that measures the affinity, or closeness, of observation samples in their natural order to their corresponding order statistics. The obtained affinity measures are utilized to control the influence of individual samples in the filtering process. Depending on the spread of the affinity function, which is controlled by a single parameter gamma, affine order-statistic filters operate effectively in various environments ranging from Gaussian to impulsive. The class of affine order-statistic filters subsumes the family of weighted order-statistic (WOS) affine fibers and the class of FIR affine filters, In this paper, we focus on a representative of the WOS affine filter class - the median affine filter - whose behavior can be tuned from that of a linear FIR filter to that of a robust median filter by narrowing the affinity function to a process referred to as medianization. The superior performance of affine order-statistic filters is demonstrated in two applications.