Primal–dual algorithm based on Gauss–Seidel scheme with application to multiplicative noise removal

Due to the strong edge preserving ability and low computational cost, the total variation (TV) regularization has been developed as one promising approach to solve the multiplicative denoising problem. In recent years, many efficient algorithms have been proposed for computing the numerical solution of TV-based convex variational models. Among these methods, the (linearized) augmented Lagrangian algorithm (ALM) and the primal–dual hybrid gradient (PDHG) algorithm are two of the most effective and most widely used techniques. In this paper, inspired by the connection of the ALM and PDHG algorithms, we develop an improved primal–dual algorithm for multiplicative noise removal. In the proposed algorithm, an auxiliary variable, which is updated by the Gauss–Seidel scheme, is introduced to accelerate the original primal–dual framework. The global convergence property of the proposed algorithm is also investigated. Numerical experiments on the multiplicative denoising show that the proposed algorithm outperforms the current state-of-the-art methods.