Neural filters: a class of filters unifying FIR and median filters

A new class of nonlinear filters called neural filters based on the threshold decomposition and neural networks is introduced. Neural filters can approximate both linear finite impulse response (FIR) filters and weighted order statistic (WOS) filters which include median, rank order, and weighted median filters. An adaptive algorithm is derived for determining optimal neural filters under the mean squared error (MSE) criterion. Experimental results demonstrate that, if the input signal is corrupted by Gaussian noise, adaptive neural filters converge to linear filters and that, if corrupted by impulsive noise, optimal neural filters become WOS filters