Convergence of the median filterings of sequences
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Suppose thatx=|x(n)|n∈ℤ is a sequence of real numbers. For eachp∈ℕ,x p =|x p (n)|n∈ℤis the resulting sequence ofx throughp times median filterings with window 2k+1. It is proved that whenp→∞, bothx (2p) andx(2 p}-1) are convergent. Thus the problem of convergence of the median filters of infinite-length sequences is completely solved.
Keywordsmedian filter non-linear filter recurrent sequence
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- 1.Gallagher, Jr. N. C., Wise, G. L., A theoretical analysis of the properties of median filters,IEEE Traw. on ASSP, 1981, 29: 1136.Google Scholar