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In this letter, a stationary-wavelet-based despeckling algorithm based on the two-sided generalized gamma distribution (GΓD) model is proposed. We first introduce the two-sided GΓD as a flexible and efficient model for the wavelet coefficients of logarithmically transformed synthetic aperture radar intensity or amplitude. The strength of the model is highlighted in terms of its fit to the data, its low computational cost, and the ease of parameter estimation. By empirical results, we then motivate the GΓD as model for the wavelet coefficients of the noise-free signal. The GΓD model parameters are estimated with moment methods, using both absolute central moments for the wavelet coefficients of the noisy signal and the noise. Finally, we exploit the prior information contained in the model by designing a Bayesian maximum a posteriori estimator for estimating the noise-free wavelet coefficients. Experimental results demonstrate the superiority of our method in terms of simultaneously reducing speckle and preserving structural details.