A variational model for PolSAR data speckle reduction based on the Wishart distribution

In this paper, we propose a variational model for polarimetric synthetic aperture radar (PolSAR) data speckle reduction, which is based on the complex Wishart distribution of the covariance or coherency matrix and multichannel total variation (TV) regularization defined for complex-valued matrices. By assuming the TV regularization to be a prior and taking the statistical distribution of the covariance matrix in each resolution element into account, the variational model for PolSAR covariance data speckle suppression, named WisTV-C, is derived from the maximum a posteriori estimate. A similar variational model for PolSAR coherency data speckle reduction, named WisTV-T, is also obtained. As far as we know, this is the first variational model for the whole PolSAR covariance or coherency matrix data despeckling. Since the model is nonconvex, a convex relaxation iterative algorithm is designed to solve the variational problem, based on the variable splitting and alternating minimization techniques. Experimental results on both simulated and real PolSAR data demonstrate that the proposed approach notably removes speckles in the extended uniform areas and, meanwhile, better preserves the spatial resolution, the details such as edges and point scatterers, and the polarimetric scattering characteristics, compared with other methods.