Median filtering by a generalized threshold decomposition

A generalization of the binary threshold decomposition property of median filters is presented. It is shown that median filtering can be implemented by decomposing the input sequence by monotone increasing threshold functions and applying median filtering to each of the sub-sequences generated by the decomposition scheme and then combining the filtered versions of the sub-sequences. The generalized threshold decomposition can lead to fewer sub-sequences compared to that obtained using conventional threshold decomposition and is applicable to bipolar signals. It can be used to obtain simpler realizations of median filters