A variational regularization model for multi-channel SAR image speckle reduction based on multiplicative-additive noise model

The multichannel image restoration is a kind of ill-posed inverse problem, which is usually solved by the vectorial variational regularization methods based on the independent and related prior information in the channels of the image.Focus on this, this paper propose a variational regularization model for multi-polarimetric SAR image speckle reduction based on multiplicative-additive noise model. Two level alternating minimization algorithm is designed for solving this new variational regularization model. According to the scattering matrix representation model of the multi-polarimetric SAR image, the amplitude coupling term of the arbitrarily two channels of the multi-polarimetric SAR image satisfies a multiplicative-additive noise model. The distribution of the two kinds of noise is determined by the correlation coefficient of the two channels. This paper establishes a variational regularization model for denoising this kind of multiplicative-additive noise. A auxiliary variable is introduced into the observe model to decompose it into an additive noise model and a multiplicative noise model. Then the variational regularization model for restoring the two channel coupling term from the multiplicative-additive noise is obtained by using the MAP method. To solve this model, it is considered as a minimization model of the primal and the auxiliary variables. Then an alternating minimization algorithm is used to solve the problem. The sub-model with respect to the primal variable is non-convex, which is convexed by a variable substitution technique. Then according to the separation of variables, the penalty method, and the iterative reweighted least squares method, the convex model is transformed into a minimization model with respect to three variables, which is solved again by an alternating minimization algorithm. On the other hand, the sub-model with respect to the auxiliary variable is quadratic convex, which can be easily solved by the Newton iteration method. In this paper, this new model is applied to the multi-polarimetric SAR image, and a fine despeckling result is obtained.