Abstract:  In order to suppress the speckle noise generated in the imaging process of synthetic aperture radar (SAR) images, a novel SAR despeckling method based on low-rank decomposition and improved non-local means was proposed. Firstly, the logarithmic processing of SAR image was carried out to convert multiplicative noise into additive noise. Then the logarithmic image was divided into low-rank image part and sparse image part with low-rank and sparse decomposition theory. After that the structure tensor of the sparse image with serious noise was analyzed to generate the attenuation factor required by the non-local means filtering, and the improved non-local average filtering was carried out to remove noise. Finally, the images were combined and the despeckling SAR image was obtained by exponential transformation. The experimental results demonstrate that，the proposed method has good ability of suppressing noise and keeping the detail better after visual evaluation, EPI and ENL.