Optimization model for multiplicative noise and blur removal based on Gaussian curvature regularization

In this paper, we focus on the restoration of images that are simultaneously blurred and corrupted by multiplicative noise. First, we introduce a variational restoration model consisting of the convex data-fitting term and the Gaussian curvature of the image as a regularizer to remove multiplicative Gamma noise because it is able to eliminate staircase effects while preserving sharp edges, textures, and other fine structures of the image. We then propose computing the minimizers of our restoration functionals by applying the augmented Lagrange multiplier method with splitting techniques. The numerical results in this paper show that our method has the potential to outperform other approaches in multiplicative noise removal with simultaneous deblurring.