An Enhanced High-Order Variational Model Based on Speckle Noise Removal With $G^0$ Distribution

Speckle noise removal problem has been researched under the framework of regularization-based approaches. The regularizer is normally defined as total variation (TV) that induces staircase effect. Although higher-order regularizer can conquer the staircase effect to some extent, it often leads to blurred. Considering the upper questions, the combination of first and second-order regularizer will be an effective and prior method to tackle speckle noise removal. So a variational model with hybrid TV and higher-order total curvature (TC) term is proposed in this paper, the data fidelity term is derived based on $G^{0}$ distribution. In order to preserve the edge detail better, the boundary detection function is combined with the regularizer. Furthermore, the Mellin transform is used to estimate the parameters of the model. To address the speckle noise removal optimization problem, alternating direction method of multipliers (ADMM) framework is employed to design a convex numerical method for the proposed model. The numerical method can be used to update the variables flexibly as required by the hybrid regularizer. The numerous experiments were performed on both synthetic and real SAR images. Compared with some classical and state-of-the-art SAR despeckling methods, experiment results demonstrate the improved performance of the proposed method, including that speckle noise can be removed effectively, and staircase effect can be prevented while preserving image feature.