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This paper introduces a new wavelet-based speckle reduction method for medical ultrasound images, which extends a recently emerged homomorphic Bayesian technique. The new method exploits interscale dependency of wavelet coefficients. For this purpose, bivariate alpha-stable distributions are proposed, which are able to better capture the heavy-tailed nature of the data. Using this new statistical model, we design a bivariate Bayesian estimator to effectively remove speckle from wavelet coefficients. Better results are obtained using the oriented two-dimensional dual-tree complex wavelet transform (2D DTCWT) which offers improved directional selectivity and near shift invariance property. To assess the performance of the proposed method, results are compared with some related earlier techniques. Both numerical and visual comparisons indicate improved speckle reduction while preserving structural features, as desired for better diagnosis in medical images.