Stochastic analysis for the recursive median filter process

Vector probability measure functions (density function) for recursively median filtered signals are found when the underlying input binary sequences are either independent identically distributed (i.i.d.) or Markov chains. The results are parametric in the window size of the filter and in the probability distribution of the input sequence. Using statistical threshold decomposition, the same results are found for discrete alphabet random sequences that are either i.i.d. or Markov chains. Some examples illustrating the efficacy of the recursive median filter relative to the nonrecursive implementation are presented. In particular, the breakdown probabilities are tabulated for both recursive and nonrecursive median filters