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1 July 1990 Some properties of order statistic filters
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Proceedings Volume 1247, Nonlinear Image Processing; (1990)
Event: Electronic Imaging: Advanced Devices and Systems, 1990, Santa Clara, CA, United States
Let X1, X2, ... be a stationary sequence of random variables with Pr(Xt less than or equal to x) = F(x), t = 1, 2, ... . Also let Xi:n(t), i = 1, ..., n, denote the i-th order statistic (OS) in the moving sample (Xt-N, ..., Xt, ..., Xt+N) of odd size n = 2N + 1. Then Yt = (summation)aiXi:n(t) with (summation)ai = 1 is an order statistics filter. In practice ai greater than or equal to 0, i = 1, ..., n. For t > N, the sequence (Yt) is also stationary. If X1, X2, ... are independent, the autocorrelation function ρ(r) = corr(Yt, Tt+r) is zero for r > n-1 and for r less than or equal to n-l can be evaluated directly in terms of the means, variances, and covariances of the OS in random samples of size n + r from F(x). In special cases several authors have observed that (Yt) produces a low-pass filter. It will be shown that this result holds generally under white noise. The effect of outliers (impulses) is also discussed.
© (1990) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Herbert A. David "Some properties of order statistic filters", Proc. SPIE 1247, Nonlinear Image Processing, (1 July 1990);


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