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Speckle reduction is a prerequisite for many ultrasound image processing tasks. In this study, the authors introduce a novel speckle suppression method for ultrasound images, based on statistical modelling of wavelet coefficients. First, the authors demonstrate that the wavelet coefficients of log-transformed ultrasound images have significantly non-Gaussian statistics and a two-dimensional heteroscedasticity exists in them. Previously, they described the overall multiscale wavelet transform of the log-transformed ultrasound images using two-dimensional generalised autoregressive conditional heteroscedastic (2D GARCH) model. In this study, they introduce a new heteroscedastic model, that is, 2D-GARCH generalised Gaussian (2D-GARCH-GG) as an extension of 2D-GARCH model. This new model can capture heavy-tailed marginal distribution and the intrascale dependencies of wavelet coefficients. Also, 2D-GARCH-GG model introduces additional flexibility in the model formulation in comparison with 2D-GARCH model, which results in better characterisation of ultrasound images subbands and improved restoration in noisy environments. In consequence, the authors introduce maximum a-posteriori estimator, based on GARCH-GG modelling to estimate the clean wavelet coefficients. In order to evaluate the performance of the proposed method in speckle suppression, they compare it with other denoising methods applied on some artificially speckled and actual ultrasound images and we verify the performance improvement in utilising the new strategies.