This paper introduces a speckle noise reduction algorithm using Bayesian estimation in the wavelet domain. The wavelet coefficients of the log-transformed signal are modeled by Laplacian distribution, while those of the log-transformed speckle are modeled by Maxwell distribution. The Bayesian maximum a posteriori (MAP) estimation is basically based on the presumption that speckle is spatially correlated within a small window. In this paper, the window size is automatically regulated depending on the statistics, such as mean and variance. Simulations are performed using synthetically real speckled ultrasound (US)) image and peppers image. The results show that the proposed method can conduct better than some of the existing methods in terms of the Peak Signal to Noise Ratio (PSNR) and the edge preservation factor.