Chapter 16: Image Restoration by Non-standard Diffusion

Many authors used different techniques for image restoration. Variational approaches are mainly used for this purpose. For example, the Mumfort-Shah is a model type for the free discontinuity in the restoration and segmentation of images. The main characteristic of this model is the isotropic diffusion, minimizing the length of the boundaries, while the classical models due to Rudin-Osher-Fatmi, minimize the total variation of the longest curves in the images. In this work we propose a new partial differential equation of order four that can be used for image restoration. This proposed model is a combination of the fast growth with respect to low curvature and the slow growth when the gradient is large. Numerical results are presented for both second and fourth order partial differential equations.