Adaptive trimmed mean filters for image restoration
An adaptive smoothing filter is proposed for reducing noise in digital signals of any dimensionality. The adaptive procedure is based on the selection of an appropriate inner or outer trimmed mean filter according to local measurements of the tail behavior (impulsivity) of the noise process. The set of trimmed means used provides robustness against a wide range of noise possibilities ranging from very shallow tailed to very heavy tailed. A Monte Carlo analysis using a family of generalized exponential distributions supports the choice of the trimmed mean selected for measured values of an impulsivity statistic. The assumption underlying the definition of the filter is that the signal to be filtered is locally smoothly varying, and that the noise process is uncorrelated and derives from an unknown, unimodal symmetric distribution. For image-processing applications, a second statistic is used to mark the location of abrupt intensity changes, or edges; in the vicinity of an edge, the trend-preserving median filter is used. Since the impulsivity and edge statistics used in defining the adaptive filter are both functions of order statistics, the extra computation required for their calculation is minimal. Examples are provided of the filter as applied to images corrupted by a variety of noises. >