Despeckling is of great interest in ultrasound medical images. The inherent limitations of acquisition techniques and systems introduce the speckles in ultrasound images. These speckles are the main factors that degrade the quality and most importantly texture information present in ultrasound images. Due to these speckles, experts may not be able to extract correct and useful information from the images. This paper presents an edge preserved despeckling approach that combines the nonsubsampled shearlet transform (NSST) with improved nonlinear diffusion equations. As a new image representation method with the different features of localization, directionality and multiscale, the NSST is utilized to provide the effective representation of the image coefficients. The anisotropic diffusion approach is applied to the noisy coarser NSST coefficients to improve the noise reduction efficiency and effectively preserves the edge features. In the diffusion process, an adaptive gray variance is also incorporated with the gradient information of eight connected neighboring pixels to preserve the edges, effectively. The performance of the proposed method is evaluated by conducting extensive simulations using both the standard test images and several ultrasound medical images. Experiments show that the proposed method provides an improvement not only in noise reduction but also in the preservation of more edges as compared to several existing methods. 
Despeckling of ultrasound medical images using nonlinear adaptive anisotropic diffusion in nonsubsampled shearlet domain