Multiplicative speckle noise which is inherently present in medical ultrasound images degrades the important clinical informations and badly affects the quality of the diagnosis. It is necessary to reduce the speckle noise to improve the visual quality of ultrasound images for better diagnoses. In this paper, a wavelet based method for despeckling of the ultrasound images is introduced where a local Wiener filter along with speckle reducing anisotropic diffusion (SRAD) filter are employed in a homomorphic framework. The signal variance in the local wiener filter is estimated from the output image of the SRAD filter. Since the size and shape of the locally adaptive window is an important issue in estimating the signal variance, nearly arbitrarily shaped windows are used for better performance. The experimental results using synthetically speckled ultrasound images show that the speckle noise is reduced to a great extent while preserving the important clinical information. In order to demonstrate the effectiveness of the proposed method, the method is compared with several other existing methods in terms of peak signal to noise ratio (PSNR), structural similarity index (SSIM), edge preservation index (β), and standard deviation to mean (S/M) ratio.