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Polarimetric SAR (PolSAR) scattering characteristics of imagery are always obtained from the second order moments estimation of multi-polarization data, that is, the estimation of covariance or coherency matrices. Due to the extra-paths that signal reflected from separate scatterers within the resolution cell has to travel, speckle noise always exists in SAR images and has a severe impact on the scattering performance, especially on single look complex images. In order to achieve high accuracy in estimating covariance or coherency matrices, three aspects are taken into consideration: (1) the edges and texture of the scene are distinct after speckle filtering; (2) the statistical characteristic should be similar to the object pixel; and (3) the polarimetric scattering signature should be preserved, in addition to speckle reduction. In this paper, a joint restriction principle is proposed to meet the requirement. Three different restriction principles are introduced to the processing of speckle filtering. First, a new template, which is more suitable for the point or line targets, is designed to ensure the morphological consistency. Then, the extent sigma filter is used to restrict the pixels in the template aforementioned to have an identical statistic characteristic. At last, a polarimetric similarity factor is applied to the same pixels above, to guarantee the similar polarimetric features amongst the optional pixels. This processing procedure is named as speckle filtering with joint restriction principle and the approach is applied to GF-3 polarimetric SAR data acquired in San Francisco, CA, USA. Its effectiveness of keeping the image sharpness and preserving the scattering mechanism as well as speckle reduction is validated by the comparison with boxcar filters and refined Lee filter. [ABSTRACT FROM AUTHOR]