Image Denoising Based on Topological Optimization and Fractional Diffusion

Edges of image will blur when the classical denoising method is used to remove noise.In order to solve this problem,a denoising method based on topological optimization and fractional diffusion is proposed.Topological derivative is taken as an indicator to pick up the edge points,on which the most optimal anisotropic diffusion coefficients are chosen.Then the original image is processed using the fractional diffusion equation.The method for choosing diffusion coefficients has the global property.Numerical experiments show that the new method can effectively remove noise and preserve such details as edges.So by combining the fractional diffusion method and topological optimization,a better denoising effect can be obtained.