A new variational approach for restoring images with multiplicative noise

This paper proposes a novel variational model for restoration of images corrupted with multiplicative noise. It combines a fractional-order total variational filter with a high-order PDE (Laplacian) norm. The combined approach is able to preserve edges while avoiding the blocky-effect in smooth regions. This strategy minimizes a certain energy subject to a fitting term derived from a maximum a posteriori (MAP). Semi-implicit gradient descent scheme is applied to efficiently finding the minimizer of the proposed functional. To improve the numerical results, we opt for an adaptive regularization parameter selection procedure for the proposed model by using the trial-and-error method. The existence and uniqueness of a solution to the proposed variational model is established. In this study parameter dependence is also discussed. Experimental results demonstrate the effectiveness of the proposed model in visual improvement as well as an increase in the peak signal-to-noise ratio comparing to corresponding PDE methods.