Weighted Iterative Truncated Mean Filter

The iterative truncated arithmetic mean (ITM) filter was proposed recently. It offers a way to estimate the sample median by simple arithmetic computing instead of the time consuming data sorting. In this paper, a rich class of filters named weighted ITM (WITM) filters are proposed. By iteratively truncating the extreme samples, the output of the WITM filter converges to the weighted median. Proper stopping criterion makes the WITM filters own merits of both the weighted mean and median filters and hence outperforms the both in some applications. Three structures are designed to enable the WITM filters being low-, band- and high-pass filters. Properties of these filters are presented and analyzed. Experimental evaluations are carried out on both synthesis and real data to verify some properties of the WITM filters.