An accurate operator splitting scheme for nonlinear diffusion filtering

Efficient numerical schemes for nonlinear diffusion filtering based on additive operator splitting (AOS) were introduced in [15]. AOS schemes are efficient and unconditionally stable, yet their accuracy is limited. Future applications of nonlinear diffusion filtering may require better accuracy at the expense of a relatively modest cost in computations and complexity. In this report we explore second order operator-splitting schemes for nonlinear diffusion filters. An accurate extension of the AOS schemes is suggested, which belongs to the alternating direction implicit (ADI) type methods, coupled with a symmetric splitting. The splitting is both additive and multiplicative, and preserves the accuracy of propagating with the Crank-Nicolson scheme in each dimension.