Some properties of order statistic filters

Herbert A. David

doi:10.1117/12.19598

1 July 1990 Some properties of order statistic filters

Herbert A. David

Proceedings Volume 1247, Nonlinear Image Processing; (1990) https://doi.org/10.1117/12.19598
Event: Electronic Imaging: Advanced Devices and Systems, 1990, Santa Clara, CA, United States

Abstract

Let X₁, X₂, ... be a stationary sequence of random variables with Pr(X_t less than or equal to x) = F(x), t = 1, 2, ... . Also let X_i:n^(t), i = 1, ..., n, denote the i-th order statistic (OS) in the moving sample (X_t-N, ..., X_t, ..., X_t+N) of odd size n = 2N + 1. Then Y_t = (summation)a_iX_i:n^(t) with (summation)ai = 1 is an order statistics filter. In practice a_i greater than or equal to 0, i = 1, ..., n. For t > N, the sequence (Y_t) is also stationary. If X₁, X₂, ... are independent, the autocorrelation function ρ(r) = corr(Y_t, T_t+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 (Y_t) 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.

Citation Download Citation

Herbert A. David "Some properties of order statistic filters", Proc. SPIE 1247, Nonlinear Image Processing, (1 July 1990); https://doi.org/10.1117/12.19598

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