Fast adaptation and performance characteristics of FIR-WOS hybrid filters

Fast adaptive algorithms are developed for training weighted order statistic (WOS) filters and FIR-WOS hybrid (FWH) filters under the mean absolute error (MAE) criterion. These algorithms are based on the threshold decomposition of real-valued signals introduced in this paper. With this method an N-length WOS filter can be implemented by thresholding the input signals at most N times independent of the accuracy used. Beside saving in computations, the proposed algorithms can be applied to process arbitrary real-valued signals directly. Performance characteristics of FWH filters in 1-D and 2-D signal restoration are investigated through computer simulations. We show that both in restoration of signals containing edges and in the case of heavy tailed nonGaussian noise, considerable improvement in performance can be achieved with FWH filters over WOS filters, Ll filters, and adaptive linear filters. Two new FWH filter design strategies are found for removal of impulsive noise and for restoration of a square wave, respectively