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In this paper, a detailed description and comparison of speckle reduction of medical ultrasound, and in particular echocardiography, is presented. Fifteen speckle reduction filters are described in a detailed fashion to facilitate implementation for research and evaluation. The filtering techniques considered include anisotropic diffusion, wavelet denoising, and local statistics. Common nomenclature and notation are adopted, to expedite comparison between approaches. Comparison of the filters is based on their application to simulated images, clinical videos, and a computational requirement analysis. The ultrasound simulation method provides a realistic model of the image acquisition process, and permits the use of a noise-free reference image for comparison. Application of objective quality metrics quantifies the preservation of image edges, overall image distortion, and improvement in image contrast. The computational analysis quantifies the number of operations required for each speckle reduction method. A speed-accuracy analysis of discretization methods for anisotropic diffusion is included. It is concluded that the optimal method is the OSRAD diffusion filter. This method is capable of strong speckle suppression, increasing the average SNRA of the simulated images by a factor of two. This method also shows favorable edge preservation and contrast improvement, and may be efficiently implemented.