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A novel three-step method to reduce speckle in Synthetic Aperture Radar (SAR) images is presented. First, an edge detector is used to detect the edge orientations in SAR images. Second, using a data processing method named empirical mode decomposition, the SAR image is smoothed along four directions: horizontal, vertical, left diagonal and right diagonal, respectively. Third, the SAR image is reconstructed such that if the edge direction is horizontal, the pixel smoothed along the horizontal direction is used to reconstruct the image, and so on; if an edge is not detected, the mean of the four directionally smoothed images is used to reconstruct the image. Application of this method to SAR images has shown that it is well balanced in the quality of visual appearance, mean preservation, edge preservation, and reduction of the standard deviation.