Output distributions of stack filters based on mirrored threshold decomposition

Author

Shmulevich, Ilya ; Paredes, José Luis ; Arce, Gonzalo R.

Author_Institution

Signal Process. Lab., Tampere Univ. of Technol., Finland

Volume

49

Issue

7

fYear

2001

fDate

7/1/2001 12:00:00 AM

Firstpage

1454

Lastpage

1460

Abstract

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 independent and identically distributed (i.i.d.) 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. An example illustrating the use of the output distribution formula is provided

Keywords

Markov processes; probability; stack filters; statistical analysis; Markov chain; binary domain; binary input signal; cumulative distribution function; deterministic finite automaton; i.i.d. input noise distribution; independent identically distributed input noise; input-output characteristics; mirrored threshold decomposition; output distribution formula; sliding window operation; stack filters; transition probabilities; Automata; Band pass filters; Contamination; Distributed computing; Distribution functions; Filtering; Nonlinear filters; Signal analysis; Signal processing; Statistical analysis;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.928698

Filename

928698