Multiplicative speckle noise is always present in synthetic aperture sonar (SAS) images, which is due to the coherent nature of scattering phenomena. Many methods that reduce speckle noise while preserving texture and detail have been developed for SAR and presented in the literature. In this paper, some speckle reduction techniques from SAR images are adapted and applied to SAS high resolution images. A comparison of different methods is performed and new improvements for traditional methods are introduced, considering image quality and better Speckle Suppression Index (SSI). These methods include mean adaptive filter, anisotropic diffusion, Lee filter, Kuan filter and a wavelet-based methodology, which are applied to real SAS high resolution (HR) data collected by NATO Underwater Research Center (NURC) during the COLOSSUS measurement campaign.