A First-Order Image Restoration Model that Promotes Image Contrast Preservation

In this paper, we propose a novel first-order variational model for image restoration. The main feature of this model lies in the fact that it helps preserve image contrasts during the image restoration process. To achieve this, we design a new regularizer that presents a lower growth rate than any power function with a positive exponent for large image gradient. Augmented Lagrangian method is employed to minimize this variational model and convergence analysis is established for the proposed algorithm. Numerical experiments are presented to demonstrate the features of the proposed model and also show the efficiency of the proposed numerical method.