An accurate operator splitting scheme for nonlinear diffusion filtering

Abstract

Efficient numerical schemes for nonlinear diffusion filtering based on additive operator splitting (AOS) were introduced in [10]. AOS schemes are efficient and unconditionally stable, yet their accuracy is low. Future applications of nonlinear diffusion filtering may require additional accuracy at the expense of a relatively modest cost in computations and complexity. To investigate the effect of higher accuracy schemes, we first examine the Crank-Nicolson and DuFort-Frankel second-order schemes in one dimension. We then extend the AOS schemes to take advantage of the higher accuracy that is achieved in one dimension, by using symmetric multiplicative splittings. Quantitative comparisons are performed for small and large time steps, as well as visual examination of images to find out whether the improvement in accuracy is noticeable.