A new class of nonlinear filters-neural filters

A class of nonlinear filters based on threshold decomposition and neural networks is defined. It is shown that these neural filters include all filters defined either by continuous functions, such as linear finite impulse response (FIR) filters, or by Boolean functions, such as generalized stack filters. Adaptive least-mean-absolute-error and adaptive least-mean-square-error algorithms are derived for determining optimal neural filters. As special cases, adaptive generalized stack and adaptive generalized weighted order statistic filtering algorithms under both error criteria are derived. Experimental results in 1D and 2D signal processing are presented to compare the performances of the adaptive neural filters and other widely used filters