A modified convex variational model for multiplicative noise removal

• Using other efficient methods to solve a convex variational model.
• An improved method for a variational is proposed.
• A new variational model which is efficient for multiplicative noise removal is proposed.

In this paper, a convex variational model for multiplicative noise removal is studied. Accelerating primal–dual method and proximal linearized alternating direction method are also discussed. An improved primal–dual method is proposed. Algorithms above produce more desired results than primal–dual algorithm when we solve the convex variational model. Inspired by the statistical property of the Gamma multiplicative noise and I-divergence, a modified convex variational model is proposed, for which the uniqueness of solution is also provided. Moreover, the property of the solution is presented. Without inner iterations, primal–dual method is efficient to the modified model, and running time can be reduced dramatically also with good restoration. When we set parameter αα to 0, the convex variational model we proposed turns into the model in Steidl and Teuber (2010). By altering αα, our model can be used for different noise level.