NONLINEAR EDGE-PRESERVING NOISE SUPPRESSION TECHNIQUES WITH APPLICATIONS IN IMAGE ENHANCEMENT (MEDRAN FILTER)

In this dissertation the design of nonlinear filters for smoothing a noisy signal with information-bearing sharp edges is considered. Classical linear filters designed to reduce noise will also smear out edges. In addition, linear filters are not effective in suppressing impulsive noise components. A simple nonlinear filter called the median filter has been used with some success as an edge-preserving smoothing technique. Although median filters are effective in suppression of impulsive noise components, they cannot suppress Gaussian-type noise sufficiently.Use of the generalized median filters in enhancement of noisy images is then considered. It is noted that generalized median filters can be categorized as selective averaging techniques, which are a class of edge-preserving filters. Consideration of the relationship between generalized median filters and a particular selective averaging technique yields some new filtering techniques, such as the very effective modified nearest neighbor filter (MNN filter). All these filters are applied in an experiment on the enhancement of noisy images, and the results are presented and discussed.We first consider some generalizations of median filters which combine properties of both linear and median filters. In particular, L-filters and M-filters are considered, motivated by robust estimators which are generalizations of the median as a location estimator. The deterministic and statistical properties of such filters are investigated. It is shown that M-filters can have better edge characteristics than can L-filters for comparable noise suppression performance. A related generalized median filter called the modified trimmed mean filter (MTM filter) is also introduced. An MTM filter generally shows better overall characteristics than a median, L- or M-filter. The concept of double-window filtering is introduced as a refinement of MTM filtering.