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A new methodology for speckle suppression of SAR images using an over-complete dictionary is presented. The approach taken is based on sparse and redundant representations by employing a combined dictionary consisting of wavelets, shearlets and learned dictionaries. Wavelets provide sparse expansions for point-like structures, shearlets provide sparse expansions for curve-like structures, and learning dictionaries are taken as obtaining the best performance on a training set. The experimental results demonstrate that the proposed algorithm provides more effective speckle reduction as well as detail preservation.