In this paper, a wavelet-based speckle-removing algorithm is represented and tested on synthetic aperture radar (SAR) images. The SAR image is first transformed using a dyadic wavelet transform. The noise in the wavelet-transformed image is modeled as an additive signal-dependent noise with Gaussian distribution. The distribution of a noise-free image in a wavelet domain is modeled as a generalized Gauss-Markov random field (GGMRF). An unsupervised stochastic model-based approach to image denoising is represented. If the observed area is homogeneous, the parameters of the Gaussian distribution and GGMRFs are estimated from incomplete data using mixtures of wavelet coefficients. An expectation-maximization algorithm is used to estimate the parameters of both noisy and noise-free images. The unknown parameters are estimated using image and noise models that are defined in the wavelet domain for heterogeneous areas. Different inter-and intrascale dependences of wavelet coefficients were used to estimate the unknown parameters. The represented wavelet-based method efficiently removes noise from SAR images.