A Novel Nonlinear Second Order Hyperbolic Partial Differential Equation-Based Image Restoration Algorithm With Directional Diffusion

Recently, variational and partial differential equation (PDE)-based algorithms have become very important for image restoration. In this study, we propose a new second order hyperbolic PDE model based on directional diffusion for image restoration. This hyperbolic PDE restoration model can simply diffuse along the edge's tangential direction in the observed image, thereby removing noise while preserving the image edges and fine details, which avoids the staircase effect in the restored image. An effective numerical scheme is proposed for handling the computation of our approach using the finite difference method. Successful image restoration experiments demonstrated that the proposed second order hyperbolic PDE-based model obtains superior performance compared with other models at preserving edges and it avoids the staircase effect.