Coupling local and nonlocal fourth-order evolution equations for image denoising

Local and nonlocal regularization methods have attracted an extensive interest in image denoising. In this paper, we propose two hybrid energy functionals that benefit from the local Laplacian regularization in homogeneous regions and the nonlocal Laplacian regularization in texture regions. The existence and uniqueness of solutions for the gradient flows, which are local and nonlocal coupled fourth-order evolution equations, are proven via the fixed point method. We consider nonlinear generalizations of the coupled equations for image denoising by proposing a new fourth-order operator that reduces the contrast losing effect of the second-order operator. The operator splitting method is adopted for the numerical implementation such that the local and nonlocal parts are handled separately. By numerical experiments, we illustrate that the proposed equations inherit advantages of the local and nonlocal methods for image denoising.