ANALYSIS AND OPTIMIZATION OF SUBSET AVERAGED MEDIAN FILTERS

By analyzing the subset averaged median (SAM) filter based on threshol d decomposition, we show that the class of SAIM filters is identical t o the class of extended threshold Boolean filters (ETBF's) with the ex tended self-dual property. This result indicates that the class of SAM filters encompasses a variety of digital filters such as linear finit e impulse response (FIR), weighted median, symmetric L-filters, and an y filter defined by a linear combination of these filters. A procedure for determining an optimum SAM filter in the mean square error (MSE) sense is developed. It is shown that the optimization of SAM filters m ay result in a FIR Wiener filter when the input is Gaussian and in a m edian-type filter for non-Gaussian inputs.