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Speckle noise is always present in Synthetic Aperture Radar (SAR) images. Many methods that reduce speckle noise while preserving texture and detail have been presented previously. In this paper, a comparison of different methods using wavelet decomposition is performed and new improvements for traditional methods are introduced. These techniques are: Wiener filtering, classical soft threshold, a new adaptive soft threshold and Bayesian reconstruction. First, speckle noise in a SAR image was analysed statistically. Then, a simulated image following these characteristics was created in order to evaluate noise reduction. The mean squared error was classified depending on the spatial characteristics of a local region. This tool gave valuable information for algorithm assessment. In the comparison, the new adaptive soft threshold method provided excellent results concerning noise reduction and detail preservation compared with classical soft threshold and Wiener methods. In addition, it gave as much noise reduction as the most sophisticated Bayesian method, but much more efficiently. Hence, the adaptive version of soft thresholding outperformed the other techniques. This study also presents a rigorous framework for speckle noise simulation and noise reduction evaluation.