A high-contrast fourth-order PDE from imaging: numerical solution by ADI splitting

We consider a nonlinear fourth-order diffusion equation that arises in denoising of image densities. We propose an alternative direction implicit (ADI) splitting method for its numerical solution. To treat the high-order and mixed derivative terms in the equation we adopt an ADI method by Hundsdorfer and Verwer to the present setting. The paper is furnished with numerical results for the evolution of simple densities and for image denoising.