Fast Numerical Solutions of Diffusion Equations in Image Processing
图像处理中扩散方程的快速数值解法

Fast algorithms for solving the 2 order nonlinear diffusion equations in image processing are presented. A linear finite difference scheme incorporating the explicit scheme and the implicit scheme is given. The stability condition of the scheme is also pgivend. Then three fast iteration algorithms including the MultiGrid (MG) method, the Alternative Direction Implicit (ADI) scheme, and the Additive Operators Splitting (AOS) schemes are discussed. Comparison of the three methods show that, the denoising performance is comparative. The MG method is a little better in denoising the smooth regions, while the ADI and the AOS schemes are simpler in realization.