Fast algorithms for training stack filters

Stack filters constitute a class of nonlinear digital filters possessing a weak superposition property. In the paper, fast algorithms for training stack filters are introduced. The first algorithm is based on a technique previously developed. Similar to the previous algorithm, this improved method requires only simple arithmetic operations-increment, decrement, and local comparison. The ε-convergence property of the fast algorithm is established. In addition, two fast training algorithms are developed for a subclass of stack filters called weighted order statistic filters. These fast algorithms are variants of the LMS and RLS algorithms in linear filters. All three fast algorithms developed exploit the repetition property of the training input. The factor of speedup is approximately the ratio between the number of quantization levels of the input and the window size