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Speckle noise reduction is an important preprocessing stage for ultrasound medical image processing. In this paper, a despeckling algorithm is proposed based on non-subsampled contourlet transform. This transform has the property of high directionality, anisotropy and translation invariance, which can be controlled by non-subsampled filter banks. This study aims to denoise the speckle noise in ultrasound images using adaptive binary morphological operations, in order to preserve edges, contours and textures. In morphological operations, structural element plays an important role for image enhancement. In this work, different shapes of structural element have been analysed and filtering parameters have been changed adaptively depending on the nature of the image and the amount of noise in the image. Experimental results of proposed method for natural images, Field II simulated images and real ultrasound images, show that the proposed method is able to preserve edges and image structural details compared with existing methods. [ABSTRACT FROM AUTHOR]