Application of iterative Jacobi method for an anisotropic diffusion in image processing

Image restoration has been an active research area. Different formulations are effective in high quality recovery. Partial Differential Equations (PDEs) have become an important tool in image processing and analysis. One of the earliest models based on PDEs is Perona-Malik model that is a kind of anisotropic diffusion (ANDI) filter. Anisotropic diffusion filter has become a valuable tool in different fields of image processing specially denoising. This filter can remove noises without degrading sharp details such as lines and edges. It is running by an iterative numerical method. Therefore, a fundamental feature of anisotropic diffusion procedure is the necessity to decide when to stop the iterations. This paper proposes the modified stopping criterion that from the viewpoints of complexity and speed is examined. Experiments show that it has acceptable speed without suffering from the problem of computational complexity.