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This letter presents the despeckling of synthetic aperture radar (SAR) images within the bandelet and contourlet domains. A model-based approach is presented for the despeckling of SAR images. The speckle-reduced estimate is found using the first-order Bayesian inference, and the best model's parameters are estimated using the second-order Bayesian inference. Synthetic and real images are used for evaluating the qualities of the despeckling methods. The experimental results showed that the combination of Bayesian inference and bandelet transform outperforms the contourlet-based despeckling algorithm using synthetic data and objective measurements.