Modeling image properties using Gaussian scale mixture (GSM) model in a multiresolution transform space is the basic idea of a denoising algorithm proposed by Portilla et al. Under this model and using the correlations between pyramid coefficients, the Bayesian least squares (BLS) of each coefficient is used to estimate its original value. In this article, we analyze and discuss the BLS-GSM algorithm, its drawbacks and benefits in more detail. An analytical parameter study of this denoising approach is provided as well. Additionally, we propose a localized version of this algorithm and experimentally show that it outperforms the original method both numerically and visually. We also show that the resulting method is state-of-the-art in terms of PSNR.