A Bayesian wavelet speckle reduction algorithm for SAR image is developed under the non-homomorphic framework. We use Normal Inverse Gaussian (NIG) function for modeling backscattered signal in wavelet domain, and Gaussian function for speckle noise (i.e. signal-dependent noise). The estimation formula of noise-free signal is derived by Bayesian maximum a posteriori (MAP) criterion. With regarding to estimation of model parameters, we introduce Multiscale Local Coefficient of Variation (MLCV) as heterogeneity measure, the histogram of which can be well fitted by logarithmic normal distribution. Based on heterogeneity measure, each coefficient in wavelet sub-band is classified into one of several different heterogeneity scenes, and NIG model parameters are computed in each class through cumulants estimation method. Experiment results show that, compared with its counterpart algorithm in homomorphic framework and its counterpart algorithm in non-homomorphic framework without heterogeneity based classification, our method has obvious advantage in terms of both subjective and objective evaluation, and has obtained satisfactory de-speckled image. A classification method of wavelet coefficients is proposed by heterogeneity measure, which could provide a new means for the research of SAR image despeckling.