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This letter presents synthetic aperture radar (SAR) image despeckling using dyadic wavelet transform. Maximum a posteriori (MAP) estimation is used to despeckle a SAR image in the wavelet domain. A wavelet transformed speckle-free image is approximated with a Gauss–Markov random field, and a Gaussian model is chosen to approximate speckle in the wavelet domain. A speckle-free wavelet coefficient is estimated with Bayesian inference using image and noise model parameters, which produce the highest evidence. The experimental results showed that the despeckling algorithm removes speckle noise in the homogeneous areas better than the state-of-the-art methods, which operate in the wavelet and image domain. The proposed method is very simple and computationally not demanding.