Abstract: In general, the edge information of an image can not be effectively preserved when traditional wavelet-based de-noising methods are adopted to reduce the speckle in synthetic aperture radar (SAR) images. In view of this problem, we propose a novel noise reducing algorithm for SAR images, which is based on edge detection of the images using directional information of double-density dual tree complex wavelet transform (DD_DTCWT). The relative variance of the directional complex wavelet coefficients of DD_DTCWT is used as a measure for edge detection. Furthermore, the adaptive threshold is calculated using the probability density function of relative variance. In such a manner, the adaptive filter in DD_DTCWT domain is realized. Experimental results demonstrate that the edge information of an image can be effectively preserved and enhanced via the proposed method in improving image edge detection and high frequency complex coefficients in main directions. Also, our proposed method outperforms the speckle reduction anisotropic diffusion (SRAD) method and bivariate shrinkage function (BSF) based on DD_DTCWT in high degree of edge preservation.