A Generalization of Median Filtering Using Linear Combinations of Order Statistics

Alan C. Bovik, Thomas S. Huang, David C. Munson

Research output: Contribution to journalArticle


We consider a class of nonlinear filters whose output is given by a linear combination of the order statistics of the input sequence. Assuming a constant signal in white noise, the coefficients in the linear combination are chosen to minimize the output MSE for several noise distributions. It is shown that the optimal order statistic filter (OSF) tends toward the median filter as the noise becomes more impulsive. The optimal OSF is applied to an actual noisy image and is shown to perform well, combining properties of both the averaging and median filters. A more general design scheme for applications involving nonconstant signals is also given.

Original languageEnglish (US)
Pages (from-to)1342-1350
Number of pages9
JournalIEEE Transactions on Acoustics, Speech, and Signal Processing
Issue number6
StatePublished - Dec 1983


ASJC Scopus subject areas

  • Signal Processing

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