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In this paper, a median based filter called relaxedmedian filter is proposed. The filter is obtained by relaxing theorder statistic for pixel substitution. Noise attenuation propertiesas well as edge and line preservation are analyzed statistically. Thetrade-off between noise elimination and detail preservation is widelyanalyzed. It is shown that relaxed median filters preserve detailsbetter than the standard median filter, and remove noise better thanother median type filters.