Coupling local and nonlocal diffusion equations for image denoising

Abstract

Due to the strong ability of restoring textures and details in images, nonlocal equations have attracted an extensive interest for image denoising. However, the lack of regularity causes residual noise in the restored images. In this paper, we propose and study an evolution equation consisting of the weighted local and the weighted nonlocal p-Laplacian equations. The existence and uniqueness of solutions for the proposed equation are proven under the assumption that the weights vanish in sets of positive measure. We also show that solutions of the proposed equation converge to the solution of the usual p-Laplacian equation if the kernel is rescaled appropriately. Comparisons with local and nonlocal diffusion equations for removing Gaussian noise in images are presented.