A New Image Restoration Algorithm Based on Variational Derivative

A new application for variational derivative to image restoration is proposed. Firstly an appropriate cost functional is chosen. To overcome the shortcoming of linear diffusion of blurring edges, the linear diffusion coefficient at each pixel is perturbed. Then, by it´s definition, F derivative can be taken as an indicator to pick out the most suitable pixels at which the linear diffusion coefficients are to be changed, and correspondingly, the optimum anisotropic diffusion coefficients associated to these pixels can also be selected. The diffusion coefficient chosen here has global property. Results of numerical experiment show the chosen pixels correspond to edges of the image. And due to the nature of anisotropic diffusion, this algorithm can remove noise and preserve edges very well as comparing to nonlinear isotropic diffusion. The peak signal-to-noise ratio and signal-to-noise ratio of the denoised image are improved 24.51% and 93.53% respectively than the original polluted image using this algorithm.