Statistics of stack filters with mirrored threshold decomposition

The output distribution formula for stack filters based on mirrored threshold decomposition is derived. This formula allows one to compute the cumulative distribution function of the output of a stack filter for a given input noise distribution. Mirrored threshold decomposition permits us to analyze the input-output characteristics of the stack filter in the binary domain. The sliding window operation of the stack filter is modeled by a deterministic finite automaton. The output distribution of the filter is obtained by interpreting the automaton as a Markov Chain whose transition probabilities depend on the probabilistic description of the binary input signal.

[1]  Edward J. Coyle,et al.  Stack filters , 1986, IEEE Trans. Acoust. Speech Signal Process..

[2]  O. Yli-Harja.  Formula for the joint distribution of stack filters , 1994, IEEE Signal Processing Letters.

[3]  Gonzalo R. Arce,et al.  Stack filters, stack smoothers, and mirrored threshold decomposition , 1999, IEEE Trans. Signal Process..

[4]  Ioannis Pitas,et al.  Nonlinear Digital Filters - Principles and Applications , 1990, The Springer International Series in Engineering and Computer Science.

[5]  Jaakko Astola,et al.  Output distributions of recursive stack filters , 1999, IEEE Signal Processing Letters.

[6]  J. Astola,et al.  Fundamentals of Nonlinear Digital Filtering , 1997 .

[7]  Jaakko Astola,et al.  Analysis of the properties of median and weighted median filters using threshold logic and stack filter representation , 1991, IEEE Trans. Signal Process..