In this paper

a new method for filtering SAR images using sparse optimization model is proposed. The algorithm based on sparse representation via an over-complete dictionary has a strong data sparseness and provides solid modeling assumptions for the data sets. First

a sparse optimization model based on structural properties of then SAR image is built by regulation. Second

a practical optimization strategy is used to design a redundancy dictionary. Then

an over-complete dictionary is constructed by employing a combined dictionary consisting of wavelets

shearlets

and a redundancy dictionary. Finally

the filtering process is realized through the solution of the multi-objective optimization problem in which the mean backscatter power is reconstructed. The experimental results demonstrate that the proposed algorithm has good de-speckling capability and better enhances image details.