The speckle in polarimetric Synthetic Aperture Radar（SAR） image has seriously affected the effectiveness in extracting information.For this reason

a novel method based on the similarity of the scattering for speckle reduction is proposed.This method combines the similarity of the scattering properties and the redundant information in SAR image

and applies the Wishart distribution of SAR data to implement the measurement of the similarity.It then averages the covariance matrices with the weights according to the similarity between the matrices

leading to efficient reduction of the speckle in SAR image.The method processes each element of the covariance matrices

given its advantage in preserving polarimetric properties.Compared with the existing methods

including the Polarimetric Whitening Filter（PWF） and the polarimetric Lee filter

the implementation result indicates that the proposed algorithm is effective in improving the performance of despeckling and details preservation.