An Accurate Operator Splitting Scheme for NonlinearDi usion

EEcient numerical schemes for nonlinear diiusion ltering based on additive operator splitting (AOS) were introduced in 15]. AOS schemes are eecient and unconditionally stable, yet their accuracy is limited. Future applications of nonlinear diiusion ltering 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 diiusion lters. 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.