THEORETICAL RESULTS ON THE PROPERTIES OF MEDIAN TYPE OPERATIONS
Abstract
Median filtering is a method of signal processing which is easily implemented on digital processors. It has recently found favor in a number of areas, such as image and speech processing, where it is known for its ability to track sharp signal edges and reduce impulsive type noise. Unfortunately, even though the median filter is easy to implement, it is nonlinear with memory and thus very difficult to analyze. Recently, however, a number of deterministic properties of one dimensional median filters have been developed. The work reported on here expands on this to the nondeterministic case in part one and the two dimensional case in part two. Specifically, the multivariate output distribution of one and two dimensional median type operations is developed, and this is used in several illustrative examples of the effects of median filtering signals plus additive white noise. In addition, some of the statistics of signals plus white impulsive noise are presented. The effects of one dimensional median filtering on signal bandwidth are discussed, and optimum root estimators are examined. The structure of two dimensional root signals (signals invariant to filtering) for separable median filters is developed. In addition, it is proved that repeated passes of a separable median filter over any image will reduce it to such a root structure except possibly in rarely occuring regions of time varying binary oscillations when larger windows are used ((GREATERTHEQ) 9 x 9). The form of these nonconvergent exceptions is also examined.
Degree
Ph.D.
Subject Area
Electrical engineering
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